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experiment works, it is important to know that unlike a dud, a live bomb is a kind of observer and that an encounter between the photon and a live bomb is a kind of observation. It can therefore collapse the photon's superposition, in which the photon is travelling along both the upper and lower paths. When it reaches the live bomb, or the detectors, however, it can only have been on one or the other. But, like the radioactive material in the box with Schrödinger's famous cat, upon its encounter with the half-silvered mirror at the beginning of the experiment, the photon, paradoxically does and does not interact with the bomb. According to the authors, the bomb both explodes and does not explode. This is only in the case of a live bomb, however. In any event, once observed by the detectors, it will have only traveled one of the paths.
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interferometer is constructed, a photon going through the second mirror from the lower path towards detector D will have a phase shift of half a wavelength compared to a photon being reflected from the upper path towards that same detector, while a photon coming from the upper path and towards detector C would have the same phase as one being reflected from the lower path towards that detector, so if the photon went through both paths, only detector C would be able to detect the photon. Thus, Detector D is able to detect a photon only in the event of a lone photon going through the second mirror (see figure 6). In other words, if the photon is in a superposition at the time it arrives at the second half-silvered mirror, it will always arrive at detector C and never at detector D.
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measurement or not) can be propagated to other devices (such as the final detectors) through a mode which, in the quantum account, is in the vacuum quantum state. In particular, in the case of the
Elitzur-Vaidman bomb-tester, it is what opens up the possibility that information about whether the bomb is functional or faulty can be propagated to the final detectors through the physical state of the R mode even though in the quantum account the R mode is in the vacuum quantum state.
1176:. They can either strengthen each other by "constructive interference", or weaken each other by "destructive interference". This is true whether the wave is in water, or a single photon in a superposition. So even though there is only one photon in the experiment, because of its encounter with the first half-silvered mirror, it acts like two. When "it" or "they" are reflected off the ordinary mirrors, it will interfere with itself as if it were two different photons.
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1252:: This will always be the outcome if a bomb is a dud, however, there is a 25% chance that this will be the outcome if the bomb is live. If the bomb is a dud, this is because the photon remained in its superposition until it reached the second half-silvered mirror and constructively interfered with itself. If the bomb is live, this is because the photon in fact took the upper path and passed through the second half-silvered mirror.
1010:" by observing it, at which time its location (or other measured property) at the moment of observation is definite. Information can then be gleaned not only about the actual state of the particle, but also other states or locations in which it "existed" before the collapse. This gleaning of information is possible even if the particle was never factually in any of the particular states or locations that are of interest.
1117:, which allows a photon to either pass through it, or be reflected off it at a 90-degree angle (see figure 3). There is equal probability it will do either. The photon enters a superposition, in which it does both. The single particle both passes through, and is reflected off the half-silvered mirror. From that moment on, the single photon exists in two different locations.
1055:, the light is absorbed and the bomb explodes. The triggers on the dud bombs have no sensor, so any light incident on the bomb will not be absorbed and will instead pass straight through. The dud bomb will not detect any photon and will not detonate. Is it possible to determine which bombs are functional and which are duds without detonating all of the live ones?
1006:". In this state, some properties of the particle, for example, its location, are not definite. While in a superposition, any and all possibilities are equally real. So, if the particle could feasibly exist in more than one location, in certain senses that are experimentally useful, it exists in all of them simultaneously. The particle's wave can later be "
1213:
mirror. At which point it will, again, have a 50/50 chance of passing through it or being reflected off it, and, subsequently, it will be detected at either of the two detectors with the same probability. This is what makes it possible for the experiment to verify the bomb is live without actually blowing it up.
975:. The idea of getting information about an object without interacting with it is not a new one. For example, there are two boxes, one of which contains something, the other of which contains nothing. If you open one box and see nothing, you know that the other contains something, without ever opening it.
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devised a method, using a sequence of polarising devices, that efficiently increases the yield rate to a level arbitrarily close to one. The key idea is to split a fraction of the photon beam into a large number of beams of very small amplitude and reflect all of them off the mirror, recombining them
1212:
If the bomb is live, there is a 50/50 chance that the photon took the upper path. If it "factually" did so, then it "counter-factually" took the lower path (see figure 7). That counter-factual event destroyed that photon and left only the photon on the upper path to arrive at the second half-silvered
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In other words, since if the bomb is live there is no possibility of interference between the two paths, a photon will always be detected in either of the two detectors, while if the bomb is a dud there will be interference which can only cause detector C to be activated, so activation of detector D
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Specifically, even if the occupation number of a mode is 0, there are two possible values that its discrete phase might take, and hence such a mode can still encode one bit of information. This is what opens up the possibility that information about a device (e.g., whether it implements a which-way
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A light-sensitive bomb is placed along the lower path. If the bomb is live, when a photon arrives, it will explode and both will be destroyed. If it is a dud, the photon will pass by unaffected (see figure 4), i.e., it will remain in superposition until it reaches a detector. To understand how this
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Figure 7: If the bomb is live, and the photon took the upper path, there is no chance of interference at the second half-silvered mirror, and so, just as was the case at the first, it has an equal chance of reflecting off it or passing through it and arriving at either detector C or D. This is the
1208:
The two detectors and the second half-silvered mirror are precisely aligned with one another. Detector C is positioned to detect the particle if the bomb is a dud and the particle traveled both paths in its superposition and then constructively interfered with itself. Due to the way in which the
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The bomb in question: the bomb is placed inside the box beforehand on the "lower path". If the bomb is live and comes into contact with a photon, it will detonate and destroy itself and the photon. If, however, the bomb is a dud, the photon passes it by and continues on its way along the lower
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Along both the upper and lower path, the particle will encounter an ordinary mirror, positioned to redirect the two routes toward one another. They then intersect at a second half-silvered mirror. On the other side, a pair of detectors are placed such that the photon can be detected by either
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With this process 25% of live bombs can be identified without being detonated, 50% will be detonated and 25% remain uncertain. By repeating the process with the uncertain ones, the ratio of identified non-detonated live bombs approaches 33% of the initial population of bombs. See
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When it reaches the second half-silvered mirror, if the photon in the experiment is behaving like a particle (in other words, if it is not in a superposition), then it has a fifty-fifty chance it will pass through or be reflected and be detected by one or the other detector.
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detector, but never by both. It is also possible that it will not be detected by either. Based on this outcome, with a live bomb, there is a 50% chance it will explode, a 25% chance it will be identified as good without exploding and a 25% chance there will be no result.
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1246:: The bomb exploded and destroyed the photon before it could be detected. This is because the photon in fact took the lower path and triggered the bomb, destroying itself in the process. There is a 50% chance that this will be the outcome if the bomb is live.
2018:
The authors state that the ability to obtain information about the bomb's functionality without ever "touching" it appears to be a paradox that, they argue, is based on the assumption that there is only a single "real" result. But according to the
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In 2016, Carsten Robens, Wolfgang Alt, Clive Emary, Dieter
Meschede, and Andrea Alberti demonstrated that the Elitzur–Vaidman bomb testing experiment can be recast in a rigorous test of the macro-realistic worldview based on the violation of the
1258:: The bomb is live but unexploded. That is because the photon in fact took the upper path and reflected off the second half-silvered mirror, something possible only because there was no photon from the lower path with which it could interfere.
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A second beam splitter: identical to the initial one. This beam splitter is positioned opposite the first, at the intersection between the lower path and upper path (after they have been redirected by the ordinary mirrors), at the exit of the
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If this is the outcome, the experiment has successfully verified that the bomb is live despite the fact that the photon never "factually" encountered the bomb itself. There is a 25% chance that this will be the outcome if the bomb is
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using ideal negative measurements. In their experiment they perform the bomb test with a single atom trapped in a polarization-synthesized optical lattice. This optical lattice enables interaction-free measurements by
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A pair of ordinary mirrors: one mirror is located on each beam path. They are positioned to redirect the photon so that the two paths intersect one another at the same position as the second beam splitter.
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Figure 6: The second half-silvered mirror and the two detectors are positioned so that the photon will only arrive at
Detector C if there is wave interference. This is only possible if the bomb is a dud.
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If the bomb "observed" the photon, it detonated and destroyed the photon on the lower path, therefore only the photon that takes the upper path will be detected, either at
Detector C or Detector D.
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2023:, each possible state of a particle's superposition is real. The authors therefore argue that the particle does actually interact with the bomb and it does explode, just not in our "world".
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Hosten, Onur; Rakher, Matthew T.; Barreiro, Julio T.; Peters, Nicholas A.; Kwiat, Paul G. (February 23, 2006). "Counterfactual quantum computation through quantum interrogation".
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If the result is 2, the experiment is repeated. If the photon continues to be observed at C and the bomb does not explode, it can eventually be concluded that the bomb is a dud.
1080:". The photon will either pass through the mirror and travel along the "lower path" inside the box, or be reflected at a 90-degree angle and travel along the box's "upper path".
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state is not interpreted as the non-existence of the photon, but is instead a photon in a "vacuum quantum state." This photon can interact with a detector and show up as
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A pair of photon detectors: located outside the box, they are aligned with the second beam-splitter. The photon can be detected at either or neither, but never both.
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The probability of exploding the bomb can be made arbitrarily small by repeating the interaction several times. It can be modelled in a convenient way with the
2995:. Asia-Pacific Physics Conference. Proceedings of the 8th Asia-Pacific Physics Conference, Taipei, Taiwan, 7–10 August 2000. River Edge, NJ: World Scientific.
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Catani, Lorenzo; Leifer, Matthew; Schmid, David; Spekkens, Robert W. (2023-09-25). "Why interference phenomena do not capture the essence of quantum theory".
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Pinto, Vinícius
Pereira; Pereira de Oliveira, Bruno; Mitsue Yasuoka, Fátima Maria; Courteille, Philippe Wilhelm; Caiado de Castro Neto, Jarbas (2023-09-24).
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Figure 3: Once the photon encounters the beam splitter it enters a superposition wherein it both passes through and reflects off the half-silvered mirror
34:
Bomb-testing problem diagram. A – photon emitter, B – bomb to be tested, C, D – photon detectors. Mirrors in the lower left and upper right corners are
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990:. The behavior of elementary particles is very different from what we experience in our macroscopic world. Their observed behavior can be that of a
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Figure 4: If the bomb is live, it will absorb the photon and detonate. If it is a dud, the photon is unaffected and continues along the lower path.
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Figure 5 As in Figure 4, the photon travels the lower path toward the bomb, but in a superposition, where it also travels the upper path.
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2173:, and Thomas Herzog performed an equivalent of the above experiment, proving interaction-free measurements are indeed possible.
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A live bomb will absorb the photon when it explodes and there will be no opportunity for the photon to interfere with itself.
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2037:, suggesting that it is a less dramatic illustration of non-classicality than other quantum phenomena like the violation of
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1287:. Assume that a box which potentially contains a bomb is defined to operate on a single probe qubit in the following way:
1451:{\textstyle {\begin{pmatrix}\cos {\epsilon }&-\sin {\epsilon }\\\sin {\epsilon }&\cos {\epsilon }\end{pmatrix}}}
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F. Kaiser, T. Coudreau, P. Milman, D.B. Ostroswsky and S. Tanzilli, Entanglement-Enabled
Delayed-Choice Experiment
932:. Since their publication, real-world experiments have confirmed that their theoretical method works as predicted.
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with the original beam afterwards. It can also be argued that this revised construction is simply equivalent to a
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P. G. Kwiat; H. Weinfurter; T. Herzog; A. Zeilinger; M. A. Kasevich (1995). "Interaction-free
Measurement".
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triggering its detonation, although there is still a 50% chance that the bomb will detonate in the effort.
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A. Peruzzo, P. Shadbolt, N. Brunner, S. Popescu and J.L. O'Brien, A Quantum
Delayed-Choice Experiment,
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Z. Blanco-Garcia and O. Rosas-Ortiz, Interaction-Free
Measurements of Optical Semitransparent Objects,
2020:
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2041:. The argument from Spekkens toy model involves the detector being able to detect a photon as either
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below for a modified experiment that can identify the live bombs with a yield rate approaching 100%.
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Carsten Robens; Wolfgang Alt; Clive Emary; Dieter
Meschede & Andrea Alberti (19 December 2016).
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iterations, and thus correctly identifying that there is a bomb without exploding it, is given by
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to verify that a bomb is functional without having to detonate it. It was conceived in 1993 by
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yet still carry information, allowing the bomb test to be interpreted in classical terms.
1642:{\textstyle R_{\epsilon }^{T}|0\rangle =\cos(T\epsilon )|0\rangle +\sin(T\epsilon )|1\rangle }
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1937:, which is arbitrarily close to 1. The probability of the bomb having exploded until then is
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2859:"Atomic "bomb testing": the Elitzur–Vaidman experiment violates the Leggett–Garg inequality"
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and the result looks much less shocking in this language; see Watanabe and Inoue (2000).
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An initial half-silvered mirror: the photon enters the box when it encounters this "
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2573:"Exploring Quantum Comprehension Through the Elitzur-Vaidman Bomb Testing Problem"
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A photon emitter: it produces a single photon for the purposes of the experiment.
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124:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
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Paul G. Kwiat; H. Weinfurter; T. Herzog; A. Zeilinger; M. Kasevich (1994).
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2033:. It has also been argued that the bomb test can be constructed within the
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Experimental demonstration of two dimensional interaction free measurement
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At the end of the circuit, the probe qubit is measured. If the outcome is
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These correspond with the following conditions of the bomb being tested:
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The following quantum circuit can be used to test if a bomb is present:
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offered an interpretation of the Elitzur–Vaidman bomb test in terms of
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2669:"Is the Quantum State Real? An Extended Review of ψ-ontology Theorems"
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can only occur if the bomb is live, whether the bomb exploded or not.
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is the box/bomb system, which measures the qubit if a bomb is present
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A light-sensitive bomb: it is not known whether it is live or a dud.
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When there is a bomb, the qubit will be transformed into the state
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2003:{\textstyle 1-\cos ^{2T}(\epsilon )\approx {\frac {\pi ^{2}}{4T}}}
1930:{\textstyle \cos ^{2T}(\epsilon )\approx 1-{\frac {\pi ^{2}}{4T}}}
959:, it is possible for the experiment to verify that the bomb works
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When there is no bomb, the qubit evolves prior to measurement as
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only way it can arrive at D, signifying a live (unexploded) bomb.
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1776:{\textstyle \cos(\epsilon )|0\rangle +\sin(\epsilon )|1\rangle }
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A photon: after being emitted, it travels through the box below.
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Feynman, Richard P.; Robert B. Leighton; Matthew Sands (1965).
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collide, the process by which they affect each other is called
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and other, more complex concepts which inspired it, including
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2391:"Experimental realization of "interaction-free" measurements"
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This is the only way that a photon can ever be detected at D.
1113:
A superposition in the bomb tester is created with an angled
2928:
The Road to Reality: A Complete Guide to the Laws of Physics
1783:, then measured by the box. The probability of measuring as
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Detector D is the key to confirming that the bomb is live.
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The bomb tester takes advantage of two characteristics of
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If there is no bomb, the qubit passes through unaffected.
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With a live bomb, there can be three possible outcomes:
2934:
G. S. Paraoanu (2006). "Interaction-free Measurement".
2633:, Springer International Publishing, pp. 129–197,
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1834:{\textstyle \sin ^{2}(\epsilon )\approx \epsilon ^{2}}
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1051:. When their triggers detect any light, even a single
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Watanabe, H.; Inoue, S. (2000). Yeong-Der Yao (ed.).
2366:"Applications of Quantum Search, Quantum Zeno Effect"
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Figure 1: An illustration of the experiment using a
1002:), their wave-like behavior implies what is called "
2477:"Can Schrodinger's Cat Collapse the Wavefunction?"
2231:"Quantum mechanical interaction-free measurements"
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1186:But that is only possible if the bomb is live.
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1294:If there is a bomb, the qubit gets measured:
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1178:But that is only true if the bomb is a dud.
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2229:Elitzur, Avshalom C.; Lev Vaidman (1993).
1235:The photon was detected at D (25% chance).
1232:The photon was detected at C (25% chance).
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1851:and the circuit will continue iterating.
1528:, there is a bomb, and if the outcome is
1490:{\textstyle \epsilon ={\frac {\pi }{2T}}}
1043:Consider a collection of light-sensitive
3820:Thought experiments in quantum mechanics
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1845:. Otherwise, the qubit will collapse to
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2518:The Feynman Lectures on Physics, Vol. 3
1156:Part 3: The second half-silvered mirror
14:
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2398:Fundamental Problems in Quantum Theory
1655:(the correct answer) with probability
1279:Improving probabilities via repetition
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2347:J. Phys.: Conf. Ser. 698:012013, 2016
978:This experiment has its roots in the
3830:Interpretations of quantum mechanics
2217:Renninger negative-result experiment
1854:The probability of obtaining result
1696:{\textstyle \sin ^{2}(T\epsilon )=1}
1229:No photon was detected (50% chance).
27:Quantum mechanics thought experiment
2667:Leifer, Matthew Saul (2014-11-05).
2520:. US: Addison-Wesley. p. 1.5.
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988:Wheeler's delayed-choice experiment
24:
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2418:10.1111/j.1749-6632.1995.tb38981.x
2013:
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429:Sum-over-histories (path integral)
115:
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45:Part of a series of articles about
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2631:Making Sense of Quantum Mechanics
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955:. By placing the particle in a
3743:Relativistic quantum mechanics
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2364:Vazirani, Umesh (2005-11-13).
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2077:
2049:
2010:, which is arbitrarily small.
1972:
1966:
1893:
1887:
1815:
1809:
1763:
1759:
1753:
1734:
1730:
1724:
1684:
1675:
1629:
1625:
1616:
1597:
1593:
1584:
1565:
1312:If the measurement outcome is
1297:If the measurement outcome is
579:Relativistic quantum mechanics
111:
104:
85:
13:
1:
3721:Quantum statistical mechanics
3498:Quantum differential calculus
3420:Delayed-choice quantum eraser
3203:Symmetry in quantum mechanics
2966:10.1103/PhysRevLett.97.180406
2222:
1058:
966:
922:interaction-free measurements
619:Quantum statistical mechanics
2627:"The de Broglie–Bohm Theory"
2577:Brazilian Journal of Physics
1256:The photon was detected at D
1250:The photon was detected at C
973:interaction-free measurement
7:
3825:Quantum information science
3523:Quantum stochastic calculus
3513:Quantum measurement problem
3435:Mach–Zehnder interferometer
2639:10.1007/978-3-319-25889-8_5
2475:Keith Bowden (1997-03-15).
2331:10.1103/PhysRevLett.74.4763
2212:Counterfactual definiteness
2205:
1039:Figure 2: Legend for Fig. 1
1030:Mach–Zehnder interferometer
1020:Mach–Zehnder interferometer
911:Elitzur–Vaidman bomb-tester
589:Quantum information science
18:Elitzur–Vaidman bomb-tester
10:
3856:
2750:10.22331/q-2023-09-25-1119
2589:10.1007/s13538-023-01366-x
2146:{\displaystyle |0\rangle }
2118:{\displaystyle |0\rangle }
2090:{\displaystyle |1\rangle }
2062:{\displaystyle |0\rangle }
2021:many-worlds interpretation
1363:{\textstyle R_{\epsilon }}
1220:
1128:
1017:
3789:
3751:
3703:
3583:Quantum complexity theory
3561:Quantum cellular automata
3536:
3468:
3402:
3315:
3279:
3266:Path integral formulation
3233:
3098:
3055:
2893:10.1007/s00340-016-6581-y
2359:Science 338:637–640, 2012
2353:Science 338:634–637, 2012
1843:small-angle approximation
1192:Part 4: Detectors C and D
1101:Part 1: The superposition
3650:Quantum machine learning
3630:Quantum key distribution
3620:Quantum image processing
3610:Quantum error correction
3460:Wheeler's delayed choice
2930:. Jonathan Cape, London.
2376:
1649:, which will measure as
1073:A "box" which contains:
624:Quantum machine learning
377:Wheeler's delayed-choice
3566:Quantum finite automata
2696:10.12743/quanta.v3i1.22
2202:and position of atoms.
2191:Leggett–Garg inequality
334:Leggett–Garg inequality
3670:Quantum neural network
2238:Foundations of Physics
2147:
2119:
2091:
2063:
2004:
1931:
1835:
1777:
1697:
1643:
1512:
1491:
1452:
1370:is the unitary matrix
1364:
1331:
1244:No photon was detected
1202:
1165:
1148:
1140:
1110:
1040:
1032:
980:double-slit experiment
125:
39:
3695:Quantum teleportation
3223:Wave–particle duality
2788:, pp. 4763–4766.
2148:
2120:
2092:
2064:
2005:
1932:
1836:
1778:
1698:
1644:
1513:
1492:
1453:
1365:
1330:
1285:quantum circuit model
1199:
1163:
1146:
1138:
1129:Further information:
1108:
1038:
1027:
1000:wave–particle duality
957:quantum superposition
953:wave–particle duality
319:Elitzur–Vaidman
309:Davisson–Germer
126:
33:
3726:Quantum field theory
3655:Quantum metamaterial
3600:Quantum cryptography
3330:Consistent histories
2926:Penrose, R. (2004).
2559:Elitzur Vaidman 1993
2544:Elitzur Vaidman 1993
2504:Elitzur Vaidman 1993
2463:Elitzur Vaidman 1993
2448:Elitzur Vaidman 1993
2129:
2101:
2073:
2045:
1941:
1868:
1793:
1715:
1659:
1546:
1534:, there is no bomb.
1502:
1463:
1374:
1347:
1318:, the bomb explodes.
1115:half-silvered mirror
1047:, of which some are
971:The bomb test is an
937:elementary particles
584:Quantum field theory
496:Consistent histories
133:Schrödinger equation
60:
3840:Quantum measurement
3711:Quantum fluctuation
3680:Quantum programming
3640:Quantum logic gates
3625:Quantum information
3605:Quantum electronics
3080:Classical mechanics
2958:2006PhRvL..97r0406P
2885:2017ApPhB.123...12R
2820:10.1038/nature04523
2812:2006Natur.439..949H
2742:2023Quant...7.1119C
2410:1995NYASA.755..383K
2313:1995PhRvL..74.4763K
2260:1993FoPh...23..987E
1563:
1518:is a large integer.
372:Stern–Gerlach
169:Classical mechanics
3835:1993 introductions
3764:in popular culture
3546:Quantum algorithms
3394:Von Neumann–Wigner
3374:Objective collapse
3085:Old quantum theory
2786:Kwiat, et al. 1995
2278:10.1007/BF00736012
2143:
2115:
2087:
2059:
2035:Spekkens toy model
2000:
1927:
1831:
1773:
1693:
1639:
1549:
1508:
1487:
1448:
1442:
1360:
1332:
1303:, the box returns
1273:§ Experiments
1203:
1166:
1149:
1141:
1111:
1041:
1033:
918:thought experiment
560:Von Neumann–Wigner
540:Objective-collapse
339:Mach–Zehnder
329:Leggett inequality
324:Franck–Hertz
174:Old quantum theory
121:
40:
3807:
3806:
3781:Quantum mysticism
3759:Schrödinger's cat
3690:Quantum simulator
3660:Quantum metrology
3588:Quantum computing
3551:Quantum amplifier
3528:Quantum spacetime
3493:Quantum cosmology
3483:Quantum chemistry
3198:Scattering theory
3146:Zero-point energy
3141:Degenerate levels
3049:Quantum mechanics
2863:Applied Physics B
2806:(7079): 949–952.
2648:978-3-319-25887-4
2307:(24): 4763–4766.
2171:Harald Weinfurter
2039:Bell inequalities
2031:Bohmian mechanics
1998:
1925:
1789:and exploding is
1485:
984:Schrödinger's cat
915:quantum mechanics
907:
906:
614:Scattering theory
594:Quantum computing
367:Schrödinger's cat
299:Bell's inequality
107:
82:
51:Quantum mechanics
16:(Redirected from
3847:
3797:
3796:
3508:Quantum geometry
3503:Quantum dynamics
3360:Superdeterminism
3256:Matrix mechanics
3111:Bra–ket notation
3042:
3035:
3028:
3019:
3018:
3014:
2985:
2951:
2915:
2914:
2904:
2878:
2854:
2848:
2847:
2795:
2789:
2783:
2774:
2773:
2735:
2715:
2709:
2708:
2698:
2688:
2664:
2658:
2657:
2656:
2655:
2619:
2613:
2607:
2601:
2600:
2568:
2562:
2556:
2547:
2541:
2532:
2531:
2513:
2507:
2501:
2492:
2491:
2489:
2488:
2479:. Archived from
2472:
2466:
2460:
2451:
2445:
2436:
2435:
2433:
2432:
2395:
2386:
2372:
2371:. EECS Berkeley.
2370:
2342:
2324:
2295:
2293:
2292:
2271:
2253:
2235:
2152:
2150:
2149:
2144:
2136:
2124:
2122:
2121:
2116:
2108:
2096:
2094:
2093:
2088:
2080:
2068:
2066:
2065:
2060:
2052:
2009:
2007:
2006:
2001:
1999:
1997:
1989:
1988:
1979:
1962:
1961:
1936:
1934:
1933:
1928:
1926:
1924:
1916:
1915:
1906:
1883:
1882:
1859:
1858:
1850:
1849:
1840:
1838:
1837:
1832:
1830:
1829:
1805:
1804:
1788:
1787:
1782:
1780:
1779:
1774:
1766:
1737:
1702:
1700:
1699:
1694:
1671:
1670:
1654:
1653:
1648:
1646:
1645:
1640:
1632:
1600:
1568:
1562:
1557:
1533:
1532:
1527:
1526:
1517:
1515:
1514:
1509:
1496:
1494:
1493:
1488:
1486:
1484:
1473:
1457:
1455:
1454:
1449:
1447:
1446:
1439:
1426:
1411:
1395:
1369:
1367:
1366:
1361:
1359:
1358:
1340:
1317:
1316:
1308:
1307:
1302:
1301:
1125:Part 2: The bomb
926:Avshalom Elitzur
899:
892:
885:
526:Superdeterminism
179:Bra–ket notation
130:
128:
127:
122:
114:
109:
108:
100:
88:
83:
81:
70:
42:
41:
36:semi-transparent
21:
3855:
3854:
3850:
3849:
3848:
3846:
3845:
3844:
3810:
3809:
3808:
3803:
3785:
3771:Wigner's friend
3747:
3738:Quantum gravity
3699:
3685:Quantum sensing
3665:Quantum network
3645:Quantum machine
3615:Quantum imaging
3578:Quantum circuit
3573:Quantum channel
3532:
3478:Quantum biology
3464:
3440:Elitzur–Vaidman
3415:Davisson–Germer
3398:
3350:Hidden-variable
3340:de Broglie–Bohm
3317:Interpretations
3311:
3275:
3229:
3116:Complementarity
3094:
3051:
3046:
3003:
2936:Phys. Rev. Lett
2923:
2921:Further reading
2918:
2855:
2851:
2796:
2792:
2784:
2777:
2716:
2712:
2665:
2661:
2653:
2651:
2649:
2620:
2616:
2608:
2604:
2569:
2565:
2557:
2550:
2542:
2535:
2528:
2514:
2510:
2502:
2495:
2486:
2484:
2473:
2469:
2461:
2454:
2446:
2439:
2430:
2428:
2393:
2387:
2383:
2379:
2368:
2322:10.1.1.561.6205
2301:Phys. Rev. Lett
2290:
2288:
2269:10.1.1.263.5508
2233:
2225:
2208:
2183:resonant cavity
2176:In 1996, Kwiat
2163:Anton Zeilinger
2159:
2132:
2130:
2127:
2126:
2104:
2102:
2099:
2098:
2076:
2074:
2071:
2070:
2048:
2046:
2043:
2042:
2016:
2014:Interpretations
1990:
1984:
1980:
1978:
1954:
1950:
1942:
1939:
1938:
1917:
1911:
1907:
1905:
1875:
1871:
1869:
1866:
1865:
1857:|0⟩
1856:
1855:
1848:|0⟩
1847:
1846:
1825:
1821:
1800:
1796:
1794:
1791:
1790:
1786:|1⟩
1785:
1784:
1762:
1733:
1716:
1713:
1712:
1709:
1666:
1662:
1660:
1657:
1656:
1652:|1⟩
1651:
1650:
1628:
1596:
1564:
1558:
1553:
1547:
1544:
1543:
1540:
1538:Case 1: No bomb
1531:|1⟩
1530:
1529:
1525:|0⟩
1524:
1523:
1503:
1500:
1499:
1477:
1472:
1464:
1461:
1460:
1441:
1440:
1435:
1427:
1422:
1413:
1412:
1407:
1396:
1391:
1378:
1377:
1375:
1372:
1371:
1354:
1350:
1348:
1345:
1344:
1338:
1315:|1⟩
1314:
1313:
1306:|0⟩
1305:
1304:
1300:|0⟩
1299:
1298:
1281:
1223:
1194:
1158:
1133:
1127:
1103:
1061:
1022:
1016:
969:
903:
874:
873:
872:
637:
629:
628:
574:
573:Advanced topics
566:
565:
564:
516:Hidden-variable
506:de Broglie–Bohm
485:
483:Interpretations
475:
474:
473:
443:
435:
434:
433:
391:
383:
382:
381:
348:
304:CHSH inequality
293:
285:
284:
283:
212:Complementarity
206:
198:
197:
196:
164:
135:
110:
99:
98:
84:
74:
69:
61:
58:
57:
28:
23:
22:
15:
12:
11:
5:
3853:
3843:
3842:
3837:
3832:
3827:
3822:
3805:
3804:
3802:
3801:
3790:
3787:
3786:
3784:
3783:
3778:
3773:
3768:
3767:
3766:
3755:
3753:
3749:
3748:
3746:
3745:
3740:
3735:
3734:
3733:
3723:
3718:
3716:Casimir effect
3713:
3707:
3705:
3701:
3700:
3698:
3697:
3692:
3687:
3682:
3677:
3675:Quantum optics
3672:
3667:
3662:
3657:
3652:
3647:
3642:
3637:
3632:
3627:
3622:
3617:
3612:
3607:
3602:
3597:
3596:
3595:
3585:
3580:
3575:
3570:
3569:
3568:
3558:
3553:
3548:
3542:
3540:
3534:
3533:
3531:
3530:
3525:
3520:
3515:
3510:
3505:
3500:
3495:
3490:
3485:
3480:
3474:
3472:
3466:
3465:
3463:
3462:
3457:
3452:
3450:Quantum eraser
3447:
3442:
3437:
3432:
3427:
3422:
3417:
3412:
3406:
3404:
3400:
3399:
3397:
3396:
3391:
3386:
3381:
3376:
3371:
3366:
3365:
3364:
3363:
3362:
3347:
3342:
3337:
3332:
3327:
3321:
3319:
3313:
3312:
3310:
3309:
3304:
3299:
3294:
3289:
3283:
3281:
3277:
3276:
3274:
3273:
3268:
3263:
3258:
3253:
3248:
3243:
3237:
3235:
3231:
3230:
3228:
3227:
3226:
3225:
3220:
3210:
3205:
3200:
3195:
3190:
3185:
3180:
3175:
3170:
3165:
3160:
3155:
3150:
3149:
3148:
3143:
3138:
3133:
3123:
3121:Density matrix
3118:
3113:
3108:
3102:
3100:
3096:
3095:
3093:
3092:
3087:
3082:
3077:
3076:
3075:
3065:
3059:
3057:
3053:
3052:
3045:
3044:
3037:
3030:
3022:
3016:
3015:
3001:
2986:
2942:(18): 180406.
2931:
2922:
2919:
2917:
2916:
2849:
2790:
2775:
2710:
2659:
2647:
2623:Bricmont, Jean
2614:
2602:
2563:
2561:, p. 994.
2548:
2546:, p. 990.
2533:
2527:978-0201021189
2526:
2508:
2506:, p. 992.
2493:
2467:
2465:, p. 991.
2452:
2450:, p. 988.
2437:
2380:
2378:
2375:
2374:
2373:
2361:
2355:
2349:
2343:
2296:
2251:hep-th/9305002
2244:(7): 987–997.
2224:
2221:
2220:
2219:
2214:
2207:
2204:
2158:
2155:
2142:
2139:
2135:
2114:
2111:
2107:
2086:
2083:
2079:
2058:
2055:
2051:
2015:
2012:
1996:
1993:
1987:
1983:
1977:
1974:
1971:
1968:
1965:
1960:
1957:
1953:
1949:
1946:
1923:
1920:
1914:
1910:
1904:
1901:
1898:
1895:
1892:
1889:
1886:
1881:
1878:
1874:
1828:
1824:
1820:
1817:
1814:
1811:
1808:
1803:
1799:
1772:
1769:
1765:
1761:
1758:
1755:
1752:
1749:
1746:
1743:
1740:
1736:
1732:
1729:
1726:
1723:
1720:
1708:
1705:
1692:
1689:
1686:
1683:
1680:
1677:
1674:
1669:
1665:
1638:
1635:
1631:
1627:
1624:
1621:
1618:
1615:
1612:
1609:
1606:
1603:
1599:
1595:
1592:
1589:
1586:
1583:
1580:
1577:
1574:
1571:
1567:
1561:
1556:
1552:
1539:
1536:
1520:
1519:
1511:{\textstyle T}
1507:
1497:
1483:
1480:
1476:
1471:
1468:
1458:
1445:
1438:
1434:
1431:
1428:
1425:
1421:
1418:
1415:
1414:
1410:
1406:
1403:
1400:
1397:
1394:
1390:
1387:
1384:
1383:
1381:
1357:
1353:
1342:
1322:
1321:
1320:
1319:
1310:
1292:
1280:
1277:
1265:
1264:
1253:
1247:
1237:
1236:
1233:
1230:
1222:
1219:
1193:
1190:
1157:
1154:
1126:
1123:
1102:
1099:
1098:
1097:
1094:
1093:
1092:
1088:
1085:
1081:
1071:
1068:
1065:
1060:
1057:
1015:
1012:
968:
965:
905:
904:
902:
901:
894:
887:
879:
876:
875:
871:
870:
865:
860:
855:
850:
845:
840:
835:
830:
825:
820:
815:
810:
805:
800:
795:
790:
785:
780:
775:
770:
765:
760:
755:
750:
745:
740:
735:
730:
725:
720:
715:
710:
705:
700:
695:
690:
685:
680:
675:
670:
665:
660:
655:
650:
645:
639:
638:
635:
634:
631:
630:
627:
626:
621:
616:
611:
609:Density matrix
606:
601:
596:
591:
586:
581:
575:
572:
571:
568:
567:
563:
562:
557:
552:
547:
542:
537:
532:
531:
530:
529:
528:
513:
508:
503:
498:
493:
487:
486:
481:
480:
477:
476:
472:
471:
466:
461:
456:
451:
445:
444:
441:
440:
437:
436:
432:
431:
426:
421:
416:
411:
406:
400:
399:
398:
392:
389:
388:
385:
384:
380:
379:
374:
369:
363:
362:
361:
360:
359:
357:Delayed-choice
352:Quantum eraser
347:
346:
341:
336:
331:
326:
321:
316:
311:
306:
301:
295:
294:
291:
290:
287:
286:
282:
281:
280:
279:
269:
264:
259:
254:
249:
244:
242:Quantum number
239:
234:
229:
224:
219:
214:
208:
207:
204:
203:
200:
199:
195:
194:
189:
183:
182:
181:
176:
171:
165:
162:
161:
158:
157:
156:
155:
150:
145:
137:
136:
131:
120:
117:
113:
106:
103:
97:
94:
91:
87:
80:
77:
73:
68:
65:
54:
53:
47:
46:
26:
9:
6:
4:
3:
2:
3852:
3841:
3838:
3836:
3833:
3831:
3828:
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3823:
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3818:
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3800:
3792:
3791:
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3663:
3661:
3658:
3656:
3653:
3651:
3648:
3646:
3643:
3641:
3638:
3636:
3635:Quantum logic
3633:
3631:
3628:
3626:
3623:
3621:
3618:
3616:
3613:
3611:
3608:
3606:
3603:
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3521:
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3516:
3514:
3511:
3509:
3506:
3504:
3501:
3499:
3496:
3494:
3491:
3489:
3488:Quantum chaos
3486:
3484:
3481:
3479:
3476:
3475:
3473:
3471:
3467:
3461:
3458:
3456:
3455:Stern–Gerlach
3453:
3451:
3448:
3446:
3443:
3441:
3438:
3436:
3433:
3431:
3428:
3426:
3423:
3421:
3418:
3416:
3413:
3411:
3408:
3407:
3405:
3401:
3395:
3392:
3390:
3389:Transactional
3387:
3385:
3382:
3380:
3379:Quantum logic
3377:
3375:
3372:
3370:
3367:
3361:
3358:
3357:
3356:
3353:
3352:
3351:
3348:
3346:
3343:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3322:
3320:
3318:
3314:
3308:
3305:
3303:
3300:
3298:
3295:
3293:
3290:
3288:
3285:
3284:
3282:
3278:
3272:
3269:
3267:
3264:
3262:
3259:
3257:
3254:
3252:
3249:
3247:
3244:
3242:
3239:
3238:
3236:
3232:
3224:
3221:
3219:
3216:
3215:
3214:
3213:Wave function
3211:
3209:
3206:
3204:
3201:
3199:
3196:
3194:
3191:
3189:
3188:Superposition
3186:
3184:
3183:Quantum state
3181:
3179:
3176:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3147:
3144:
3142:
3139:
3137:
3136:Excited state
3134:
3132:
3129:
3128:
3127:
3124:
3122:
3119:
3117:
3114:
3112:
3109:
3107:
3104:
3103:
3101:
3097:
3091:
3088:
3086:
3083:
3081:
3078:
3074:
3071:
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3069:
3066:
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3058:
3054:
3050:
3043:
3038:
3036:
3031:
3029:
3024:
3023:
3020:
3012:
3008:
3004:
3002:9789810245573
2998:
2994:
2993:
2987:
2983:
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2971:
2967:
2963:
2959:
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2759:
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2734:
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2721:
2714:
2706:
2702:
2697:
2692:
2687:
2682:
2678:
2674:
2670:
2663:
2650:
2644:
2640:
2636:
2632:
2628:
2624:
2618:
2611:
2610:Vazirani 2005
2606:
2598:
2594:
2590:
2586:
2582:
2578:
2574:
2567:
2560:
2555:
2553:
2545:
2540:
2538:
2529:
2523:
2519:
2512:
2505:
2500:
2498:
2483:on 2007-10-16
2482:
2478:
2471:
2464:
2459:
2457:
2449:
2444:
2442:
2427:
2423:
2419:
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2411:
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2227:
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2213:
2210:
2209:
2203:
2201:
2197:
2192:
2186:
2184:
2179:
2174:
2172:
2168:
2164:
2154:
2137:
2109:
2081:
2053:
2040:
2036:
2032:
2028:
2027:Jean Bricmont
2024:
2022:
2011:
1994:
1991:
1985:
1981:
1975:
1969:
1963:
1958:
1955:
1951:
1947:
1944:
1921:
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1912:
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1890:
1884:
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1234:
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1210:
1206:
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1145:
1137:
1132:
1122:
1118:
1116:
1107:
1095:
1089:
1086:
1082:
1079:
1078:beam splitter
1075:
1074:
1072:
1069:
1066:
1063:
1062:
1056:
1054:
1050:
1046:
1037:
1031:
1026:
1021:
1011:
1009:
1005:
1004:superposition
1001:
997:
993:
989:
985:
981:
976:
974:
964:
962:
958:
954:
950:
946:
942:
938:
933:
931:
927:
923:
919:
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912:
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893:
888:
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877:
869:
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819:
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809:
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804:
801:
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796:
794:
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789:
786:
784:
781:
779:
776:
774:
771:
769:
766:
764:
761:
759:
756:
754:
751:
749:
746:
744:
741:
739:
736:
734:
731:
729:
726:
724:
721:
719:
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714:
711:
709:
706:
704:
701:
699:
696:
694:
691:
689:
686:
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681:
679:
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674:
671:
669:
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664:
661:
659:
656:
654:
651:
649:
646:
644:
641:
640:
633:
632:
625:
622:
620:
617:
615:
612:
610:
607:
605:
602:
600:
599:Quantum chaos
597:
595:
592:
590:
587:
585:
582:
580:
577:
576:
570:
569:
561:
558:
556:
555:Transactional
553:
551:
548:
546:
545:Quantum logic
543:
541:
538:
536:
533:
527:
524:
523:
522:
519:
518:
517:
514:
512:
509:
507:
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492:
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484:
479:
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467:
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430:
427:
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420:
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412:
410:
407:
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402:
401:
397:
394:
393:
387:
386:
378:
375:
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370:
368:
365:
364:
358:
355:
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353:
350:
349:
345:
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340:
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335:
332:
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327:
325:
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320:
317:
315:
312:
310:
307:
305:
302:
300:
297:
296:
289:
288:
278:
275:
274:
273:
272:Wave function
270:
268:
265:
263:
260:
258:
255:
253:
252:Superposition
250:
248:
245:
243:
240:
238:
235:
233:
230:
228:
225:
223:
220:
218:
215:
213:
210:
209:
202:
201:
193:
190:
188:
185:
184:
180:
177:
175:
172:
170:
167:
166:
160:
159:
154:
151:
149:
146:
144:
141:
140:
139:
138:
134:
101:
95:
78:
75:
71:
63:
56:
55:
52:
49:
48:
44:
43:
37:
32:
19:
3518:Quantum mind
3439:
3430:Franck–Hertz
3292:Klein–Gordon
3241:Formulations
3234:Formulations
3163:Interference
3153:Entanglement
3131:Ground state
3126:Energy level
3099:Fundamentals
3063:Introduction
2991:
2939:
2935:
2927:
2866:
2862:
2852:
2803:
2799:
2793:
2769:
2723:
2719:
2713:
2676:
2672:
2662:
2652:, retrieved
2630:
2617:
2605:
2580:
2576:
2566:
2517:
2511:
2485:. Retrieved
2481:the original
2470:
2429:. Retrieved
2401:
2397:
2384:
2304:
2300:
2289:. Retrieved
2241:
2237:
2187:
2177:
2175:
2160:
2097:, where the
2025:
2017:
1861:
1853:
1710:
1707:Case 2: Bomb
1541:
1521:
1333:
1323:
1282:
1269:
1266:
1259:
1255:
1249:
1243:
1238:
1224:
1215:
1211:
1207:
1204:
1185:
1182:
1177:
1174:interference
1167:
1150:
1119:
1112:
1042:
1014:How it works
977:
970:
960:
934:
910:
908:
454:Klein–Gordon
390:Formulations
318:
227:Energy level
222:Entanglement
205:Fundamentals
192:Interference
143:Introduction
3776:EPR paradox
3556:Quantum bus
3425:Double-slit
3403:Experiments
3369:Many-worlds
3307:Schrödinger
3271:Phase space
3261:Schrödinger
3251:Interaction
3208:Uncertainty
3178:Nonlocality
3173:Measurement
3168:Decoherence
3158:Hamiltonian
2404:: 383–393.
2157:Experiments
949:nonlocality
930:Lev Vaidman
843:von Neumann
828:Schrödinger
604:EPR paradox
535:Many-worlds
469:Schrödinger
424:Schrödinger
419:Phase-space
409:Interaction
314:Double-slit
292:Experiments
267:Uncertainty
237:Nonlocality
232:Measurement
217:Decoherence
187:Hamiltonian
3814:Categories
3704:Extensions
3538:Technology
3384:Relational
3335:Copenhagen
3246:Heisenberg
3193:Tunnelling
3056:Background
2876:1609.06218
2733:2111.13727
2654:2021-02-23
2583:(6): 152.
2487:2007-12-08
2431:2012-05-07
2291:2014-04-01
2223:References
2196:entangling
2167:Paul Kwiat
1059:Components
1018:See also:
967:Background
939:, such as
920:that uses
838:Sommerfeld
753:Heisenberg
748:Gutzwiller
688:de Broglie
636:Scientists
550:Relational
501:Copenhagen
404:Heisenberg
262:Tunnelling
163:Background
3410:Bell test
3280:Equations
3106:Born rule
3011:261335173
2949:0804.0523
2869:(1): 12.
2828:0028-0836
2766:244715049
2758:2521-327X
2705:1314-7374
2686:1409.1570
2679:(1): 67.
2597:1678-4448
2317:CiteSeerX
2264:CiteSeerX
2161:In 1994,
2141:⟩
2113:⟩
2085:⟩
2057:⟩
1982:π
1976:≈
1970:ϵ
1964:
1948:−
1909:π
1903:−
1897:≈
1891:ϵ
1885:
1823:ϵ
1819:≈
1813:ϵ
1807:
1771:⟩
1757:ϵ
1751:
1742:⟩
1728:ϵ
1722:
1682:ϵ
1673:
1637:⟩
1623:ϵ
1614:
1605:⟩
1591:ϵ
1582:
1573:⟩
1555:ϵ
1475:π
1467:ϵ
1437:ϵ
1433:
1424:ϵ
1420:
1409:ϵ
1405:
1399:−
1393:ϵ
1389:
1356:ϵ
1168:When two
1131:Cat state
1008:collapsed
945:electrons
868:Zeilinger
713:Ehrenfest
442:Equations
119:⟩
116:Ψ
105:^
93:⟩
90:Ψ
67:ℏ
3799:Category
3593:Timeline
3345:Ensemble
3325:Bayesian
3218:Collapse
3090:Glossary
3073:Timeline
2982:24376135
2974:17155523
2911:32214686
2836:16495993
2726:: 1119.
2625:(2016),
2426:84867106
2339:10058593
2286:18707734
2206:See also
996:particle
994:or of a
793:Millikan
718:Einstein
703:Davisson
658:Blackett
643:Aharonov
511:Ensemble
491:Bayesian
396:Overview
277:Collapse
257:Symmetry
148:Glossary
3752:Related
3731:History
3470:Science
3302:Rydberg
3068:History
2954:Bibcode
2902:7064022
2881:Bibcode
2844:3042464
2808:Bibcode
2738:Bibcode
2720:Quantum
2406:Bibcode
2309:Bibcode
2256:Bibcode
1841:by the
1334:Where:
1221:Results
961:without
941:photons
833:Simmons
823:Rydberg
788:Moseley
768:Kramers
758:Hilbert
743:Glauber
738:Feynman
723:Everett
693:Compton
464:Rydberg
153:History
3445:Popper
3009:
2999:
2980:
2972:
2909:
2899:
2842:
2834:
2826:
2800:Nature
2764:
2756:
2703:
2673:Quanta
2645:
2595:
2524:
2424:
2337:
2319:
2284:
2266:
2178:et al.
1860:after
1053:photon
986:, and
863:Zeeman
858:Wigner
808:Planck
778:Landau
763:Jordan
414:Matrix
344:Popper
3355:Local
3297:Pauli
3287:Dirac
2978:S2CID
2944:arXiv
2871:arXiv
2840:S2CID
2762:S2CID
2728:arXiv
2681:arXiv
2422:S2CID
2394:(PDF)
2377:Notes
2369:(PDF)
2282:S2CID
2246:arXiv
2234:(PDF)
1263:live.
1170:waves
1084:path.
1045:bombs
998:(see
913:is a
818:Raman
803:Pauli
798:Onnes
733:Fermi
708:Debye
698:Dirac
663:Bloch
653:Bethe
521:Local
459:Pauli
449:Dirac
247:State
3007:OCLC
2997:ISBN
2970:PMID
2907:PMID
2832:PMID
2824:ISSN
2754:ISSN
2701:ISSN
2643:ISBN
2593:ISSN
2522:ISBN
2335:PMID
2200:spin
2198:the
2069:and
1091:box.
1049:duds
992:wave
951:and
928:and
909:The
853:Wien
848:Weyl
813:Rabi
783:Laue
773:Lamb
728:Fock
683:Bose
678:Born
673:Bohr
668:Bohm
648:Bell
2962:doi
2897:PMC
2889:doi
2867:123
2816:doi
2804:439
2746:doi
2691:doi
2635:doi
2585:doi
2414:doi
2402:755
2327:doi
2274:doi
1952:cos
1873:cos
1798:sin
1748:sin
1719:cos
1664:sin
1611:sin
1579:cos
1430:cos
1417:sin
1402:sin
1386:cos
943:or
3816::
3005:.
2976:.
2968:.
2960:.
2952:.
2940:97
2938:.
2905:.
2895:.
2887:.
2879:.
2865:.
2861:.
2838:.
2830:.
2822:.
2814:.
2802:.
2778:^
2768:.
2760:.
2752:.
2744:.
2736:.
2722:.
2699:.
2689:.
2675:.
2671:.
2641:,
2629:,
2591:.
2581:53
2579:.
2575:.
2551:^
2536:^
2496:^
2455:^
2440:^
2420:.
2412:.
2400:.
2396:.
2333:.
2325:.
2315:.
2305:74
2303:.
2280:.
2272:.
2262:.
2254:.
2242:23
2240:.
2236:.
2169:,
2165:,
1703:.
947::
3041:e
3034:t
3027:v
3013:.
2984:.
2964::
2956::
2946::
2913:.
2891::
2883::
2873::
2846:.
2818::
2810::
2748::
2740::
2730::
2724:7
2707:.
2693::
2683::
2677:3
2637::
2612:.
2599:.
2587::
2530:.
2490:.
2434:.
2416::
2408::
2341:.
2329::
2311::
2294:.
2276::
2258::
2248::
2138:0
2134:|
2110:0
2106:|
2082:1
2078:|
2054:0
2050:|
1995:T
1992:4
1986:2
1973:)
1967:(
1959:T
1956:2
1945:1
1922:T
1919:4
1913:2
1900:1
1894:)
1888:(
1880:T
1877:2
1862:T
1827:2
1816:)
1810:(
1802:2
1768:1
1764:|
1760:)
1754:(
1745:+
1739:0
1735:|
1731:)
1725:(
1691:1
1688:=
1685:)
1679:T
1676:(
1668:2
1634:1
1630:|
1626:)
1620:T
1617:(
1608:+
1602:0
1598:|
1594:)
1588:T
1585:(
1576:=
1570:0
1566:|
1560:T
1551:R
1506:T
1482:T
1479:2
1470:=
1444:)
1380:(
1352:R
1339:B
1309:.
898:e
891:t
884:v
112:|
102:H
96:=
86:|
79:t
76:d
72:d
64:i
38:.
20:)
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