Bram Gaasbeek
The delayed choice experiments are a collection of experiments where the counterintuitive laws of quantum mechanics are manifested in a very striking way. Although the delayed choice experiments can be very accurately described with the standard framework of quantum optics, a more didactical and intuitive explanation seems not to have been given so far. In this note, we fill that gap.
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The delayed-choice quantum eraser has long been a subject of controversy, and has been looked at as being incomprehensible to having retro-causal effect in time. Here the delayed-choice quantum eraser is theoretically analyzed using standard quantum mechanics. Employing Mach-Zehnder interferometer, instead of a conventional two-slit interference, brings in surprising clarity. Some common mistakes in interpreting the experiment are pointed out. It is demonstrated that in the delayed mode there is no which-way information present after the particle is registered on the screen or the final detect…
A critical note on some of the existing proposals for performing the "delayed choice" experiment is placed. By abandoning the original idea and intention, some modern theoretical proposals and experimental evidence are simply incorrectly understood/interpreted. In effect, the Complementarity principle remains practically intact.
We describe a cryptographic protocol in which Wheeler's delayed choice experiment is used to generate the key distribution. The protocol, which uses photons polarized only along one axis, is secure against general attacks.
A shortcoming in the authors' interpretation of this beautiful new experiment is pointed out and briefly discussed.
By slight modifying of the delayed-choice experiment, it is argued that the quantum wave function must be interpreted as real physical entity; With this interpretation in mind, multiple least action paths due to uncertainty leads us to new perspective on the Compton wavelength and the uncertainty principle itself.
Quantum and classical models for delayed choice entanglement swapping by postselection of measurements are discussed.
Delayed Choice Quantum Eraser Experiment Revisited: Causality and Informational Coherence
本文通过延迟选择量子擦除实验，利用单光子干涉检测区分因果性和信息一致性假说，无需后选择。
Comment on [R.L. Ingraham, Phys. Rev. A 50, 4502 (1994)]. Ingraham suggested ``a delayed-choice experiment with partial, controllable memory erasing''. It is shown that he cannot be right since his predictions contradict relativistic causality. A subtle quantum effect which was overlooked by Ingraham is explained.
This paper shows how one can construe the experimental results in a way that does not involve effects that precede their causes.
A realizable delayed-choice quantum eraser, using a modified Mach-Zehnder (MZ) interferometer and polarization entangled photons, is theoretically analyzed here. The signal photon goes through a modified MZ interferometer, and the polarization of the idler photon provides path information for the signal photon. The setup is very similar to the delayed-choice quantum eraser experimentally studied by the Vienna group. In the class of quantum erasers with discrete output states, it is easy to see that the delayed mode leaves no choice for the experimenter. The which-way information is always eras…
It is pointed out that a slight variation on the Wheeler Delayed Choice Experiment presents the same challenge to orthodox quantum mechanics as Maudlin-type contingent absorber experiments present to the Transactional Interpretation (TI). Therefore, the latter cannot be used as a basis for refutation of TI.
We propose a new signaling system using the experimental setup of Wheeler's delayed-choice experiment previously carried out. In the delayed-choice experiment, the experimental setup shows a wave property or a particle property at the time when the experimental conditions of the wave-particle duality of photons are chosen. Choice signals can be used as transmitting signals and the wave-particle duality of photons is used as receiving signals. For example, if we choose the wave property of a photon as a transmitting signal, we detect the interference of the wave at the detector that can be used…
Wheeler has strikingly illustrated the wave-particle duality by the delayed-choice thought experiment, in which the configuration of a 2-path interferometer is chosen after a single-photon light-pulsed has entered it. We present a quantitative theoretical analysis of an experimental realization of Wheeler's proposal.
Quantum superposition is the cornerstone of quantum mechanics, where interference fringes originate in the self-interference of a single photon via indistinguishable photon characteristics. Wheeler delayed-choice experiments have been extensively studied for the wave-particle duality over the last several decades to understand the complementarity theory of quantum mechanics. The heart of the delayed-choice quantum eraser is in the mutually exclusive quantum feature violating the cause-effect relation. Here, we experimentally demonstrate the quantum eraser using coherent photon pairs by the del…
We present a computer simulation model of Wheeler's delayed choice experiment that is a one-to-one copy of an experiment reported recently (V. Jacques {\sl et al.}, Science 315, 966 (2007)). The model is solely based on experimental facts, satisfies Einstein's criterion of local causality and does not rely on any concept of quantum theory. Nevertheless, the simulation model reproduces the averages as obtained from the quantum theoretical description of Wheeler's delayed choice experiment. Our results prove that it is possible to give a particle-only description of Wheeler's delayed choice expe…
We study for a composite quantum system with a quantum Turing architecture the temporal non-locality of quantum mechanics by using the temporal Bell inequality, which will be derived for a discretized network dynamics by identifying the subsystem indices with (discrete) parameter time. However, the direct ``observation'' of the quantum system will lead to no violation of the temporal Bell inequality and to consistent histories of any subsystem. Its violation can be demonstrated, though, for a delayed-choice measurement.
Wheeler's delayed-choice experiment investigates the indeterminacy of wave-particle duality and the role played by the measurement apparatus in quantum theory. Due to the inconsistency with classical physics, it has been generally believed that it is not possible to reproduce the delayed-choice experiment using a hidden variable theory. Recently, it was shown that this assumption was incorrect, and in fact Wheeler's delayed-choice experiment can be explained by a causal two dimensional hidden-variable theory [R. Chaves, G. B. Lemos, and J. Pienaar, Phys. Rev. Lett. 120, 190401 (2018)]. Here, w…
This paper reports a "delayed choice quantum eraser" experiment proposed by Scully and Drühl in 1982. The experimental results demonstrated the possibility of simultaneously observing both particle-like and wave-like behavior of a quantum via quantum entanglement. The which-path or both-path information of a quantum can be erased or marked by its entangled twin even after the registration of the quantum.
There is a very common fallacy, here called the separation fallacy, that is involved in the interpretation of quantum experiments involving a certain type of separation such as the: double-slit experiments, which-way interferometer experiments, polarization analyzer experiments, Stern-Gerlach experiments, and quantum eraser experiments. It is the separation fallacy that leads not only to flawed textbook accounts of these experiments but to flawed inferences about retrocausality in the context of "delayed choice" versions of separation experiments.
Wheeler's delayed-choice experiment was conceived to illustrate the paradoxical nature of wave-particle duality in quantum mechanics. In the experiment, quantum light can exhibit either wave-like interference patterns or particle-like anti-correlations, depending upon the (possibly delayed) choice of the experimenter. A variant known as the quantum eraser uses entangled light to recover the lost interference in a seemingly nonlocal and retrocausal manner. Although it is believed that this behavior is incompatible with classical physics, here we show that the observed quantum phenomena can be r…
A macroscopic delayed-choice quantum eraser using a commercial laser
本文利用商用连续波激光器和非干涉马赫-曾德尔干涉仪实验演示了宏观延迟选择量子擦除器，验证了宏观尺度下的量子叠加，为因果关系问题提供新视角。
We report on a delayed-choice quantum eraser experiment based on a two-photon imaging scheme using entangled photon pairs. After the detection of a photon which passed through a double-slit, a random delayed choice is made to erase or not erase the which-path information by the measurement of its distant entangled twin; the particle-like and wave-like behavior of the photon are then recorded simultaneously and respectively by only one set of joint detection devices. The present eraser takes advantage of two-photon imaging. The complete which-path information of a photon is transferred to its d…
Delayed choice and quantum eraser experiments have attracted much interest recently, both theoretically and experimentally. In particular, they have prompted suggestions that quantum mechanics involves acausal effects. Using a recently developed approach which takes apparatus into account, we present a detailed analysis of various double-slit experiments to show that this is never the case. Instead, quantum experiments can be described in terms of a novel concept of time called stages. These can cut across the conventional linear time parameter as experienced in the laboratory and appear to vi…
We propose and experimentally demonstrate a two-fold quantum delayed-choice experiment where wave or particle nature of a superconducting interfering device can be post-selected twice after the interferometer. The wave-particle complementarity is controlled by a quantum which-path detector (WPD) in a superposition of its on and off states implemented through a superconducting cavity. The WPD projected to its on state records which-path information, which manifests the particle nature and destroys the interference associated with wave nature of the system. In our experiment, we can recover the …
It is well known that Wheeler proposed several delayed choice experiments in order to show the impossibility to speak of the way a quantum system behaves before being detected. In a double-slit experiment, when do photons decide to travel by one way or by two ways? Delayed choice experiments seem to indicate that, strangely, it is possible to change the decision of the photons until the very last moment before they are detected. This led Wheeler to his famous sentence: No elementary quantum phenomenon is a phenomenon until it is a registered phenomenon, brought to a close by an irreversible ac…
Wave-particle duality constitutes one of the most intriguing features in quantum physics. A well-known gedanken experiment that provides evidence for this is the Wheeler's delayed-choice experiment based on a Mach-Zehnder interferometer. Many different versions of delayed-choice experiments have been conducted with both classical and quantum detecting devices. Recently, it was proposed that the delayed-choice experiment could be devised from the perspective of device-independent prepare-and-measure scenario. In our work, we experimentally realize this modified version with a deterministic sing…
John Wheeler devised a gedanken experiment in which a piece of apparatus can be altered just before the arrival of particle, and this ``delayed choice'' can, seemingly, alter the quantum state of the particle at a much earlier time, long before the choice is made. A slightly different gedanken experiment, which exhibits the same conceptual difficulty, is analyzed using the techniques of consistent history quantum theory. The idea that the future influences the past disappears when proper account is taken of the diversity of possible quantum descriptions of the world, and their mutual compatibi…
Wheeler's delayed choice experiment, a well known manifestation of the complementarity principle, has proved somewhat difficult to physically interpret. We show that, restated in quantum field theoretic language, the experiment submits to a simple explanation: that wave- or particle-nature is imposed not at the slit plane but at the detector system. The intepretational difficulty conventionally encountered is due to the assumption of enforcement of complementarity at the former.
We construct a quantum bit commitment scheme using a double-slit setup similar to Wheeler's delayed choice experiment. Bob sends photons toward the double-slit, and Alice commits by determining either the slit from which each photon emerges (for $b=0$), or its landing position on a screen (for $b=1$). Since the photon's wave front expands at the speed of light, Alice cannot delay the detection indefinitely, or it would very soon be out of her control no matter how much resources she has.
Quantum systems exhibit particle-like or wave-like behaviour depending on the experimental apparatus they are confronted by. This wave-particle duality is at the heart of quantum mechanics, and is fully captured in Wheeler's famous delayed choice gedanken experiment. In this variant of the double slit experiment, the observer chooses to test either the particle or wave nature of a photon after it has passed through the slits. Here we report on a quantum delayed choice experiment, based on a quantum controlled beam-splitter, in which both particle and wave behaviours can be investigated simulta…
It is demonstrated that 'quantum eraser' (QE) experiments do not erase any information. Nor do they demonstrate retrocausation or 'temporal nonlocality' in their 'delayed choice' form, beyond standard EPR correlations. It is shown that the erroneous erasure claims arise from assuming that the improper mixed state of the signal photon physically prefers either the 'which way' or 'both ways' basis, when no such preference is warranted. The latter point is illustrated through comparison of the QE spatial state space with the spin-1/2 space of particles in the EPR-spin experiment.
Delayed choice experiments: An analysis in forward time
本文基于教科书量子力学，前向时间分析了Wheeler经典思想实验和延迟量子擦除器，证明无需未来信息即可解释结果，且改变时间顺序的修改版会导致相同最终状态，说明场景在操作意义上完全等价。
Wheeler's delayed-choice experiment delays the decision to observe either the wave or particle behavior of a photon until after it has entered the interferometer, and the quantum delayed-choice experiment provides the possibility of observing the wave and particle behavior simultaneously by introducing quantum control device. We here propose a modified quantum delayed-choice experiment without quantum control or entanglement assistance, in which a photon can be prepared in a wave-particle superposition state and the morphing behavior of wave-to-particle transition can be observed easily. It is…
According to Quantum Mechanics, the particles can exhibit either particle properties or wave properties depending on the experimental set up (wave-particle dualism). A special behavior occurs for a system of two entangled particles 1 and 2 that propagate along two different directions in the space. In such a case, the entangled particle 2 should exhibit either the particle behavior or the wave behavior depending on the kind of measurement that is performed on particle 1 whatever is the actual distance between the two particles. The apparently surprising fact is that the "choice" of what kind o…
Structural constraint on delayed-choice quantum eraser architectures
通过引入概率约束，证明延迟选择量子擦除器架构中四个直观属性不能同时满足，从而对方案进行分类并阐明条件干涉图样的产生机制。
It is possible to find the nonlocality type of correlations between particle pairs retrospectively, matched with the outcomes of a future entangling measurement. But this does not imply nonlocality in subensembles of product pairs, nor does it imply an influence propagating backwards in time.
The conventional explanation of delayed-choice experiments appears to violate our causal intuition at the quantum level. I reanalyze these experiments using time-reversed and time-symmetric formulations of quantum mechanics. The time-reversed formulation does not give the same experimental predictions. The time-symmetric formulation gives the same experimental predictions but actually violates our causal intuition at the quantum level. I explore the reasons why our causal intuition may be wrong at the quantum level, suggest how conventional causation might be recovered in the classical limit, …
In a delayed-choice quantum eraser, interference fringes are obtained by erasing which-way information after the interfering particle has already been irreversibly detected. Following an introductory review of delayed-choice experiments and quantum erasure, we describe the experimental realization of an optical delayed-choice quantum eraser, suitable for advanced undergraduates, based on polarization-entangled pairs of single photons. In our experiment, the delay of the erasure is implemented using two different setups. The first setup employs an arrangement of mirrors to increase the optical …
The wave-particle duality dates back to Einstein's explanation of the photoelectric effect through quanta of light and de Broglie's hypothesis of matter waves. Quantum mechanics uses an abstract description for the behavior of physical systems such as photons, electrons, or atoms. Whether quantum predictions for single systems in an interferometric experiment allow an intuitive understanding in terms of the particle or wave picture, depends on the specific configuration which is being used. In principle, this leaves open the possibility that quantum systems always either behave definitely as a…
We propose a scheme feasible with current technology to implement a quantum delayed-choice experiment in the realm of cavity QED. Our scheme uses two-level atoms interacting on and off resonantly with a single mode of a high Q cavity. At the end of the protocol, the state of the cavity returns to its ground state, allowing new sequential operations. The particle and wave behavior, which are verified in a single experimental setup, are postselected after the atomic states are selectively detected.
Building on Peres's idea of "Delayed-choice for extanglement swapping" we show that even the degree to which quantum systems were entangled can be defined after they have been registered and may even not exist any more. This does not arise as a paradox if the quantum state is viewed as just a representative of information. Moreover such a view gives a natural quantification of the complementarity between the measure of information about the input state for teleportation and the amount of entanglement of the resulting swapped entangled state.
We report an experimental test of complementarity using clock-triggered single-photon pulses emitted by an individual N-V color center in a diamond nanocrystal. The single photons are sent into a Mach-Zehnder interferometer with an output beamsplitter of adjustable reflection coefficient R. In addition, the choice of introducing or removing this beamsplitter is random and relativistically space-like separated from the entering of the photon inside the interferometer, as required for the Wheeler's delayed-choice regime. Each set value of R allows us to observe interference with visibility V and…
We propose a simple implementation scheme of quantum delayed-choice experiment in linear optical system without initial entanglement resource. By choosing different detecting devices, one can selectively observe the photon's different behaviors after the photon has been passed the Mach-Zehnder interferometer. The scheme shows that the photon's wave behavior and particle behavior can be observed with a single experimental setup by postselection, that is, the photon can show the superposition behavior of wave and particle. Especially, we compare the wave-particle superposition behavior and the w…
A Standard Quantum Mechanical Treatment to Rationalize the Delayed-Choice Quantum Eraser
本文用标准量子力学解释延迟选择量子擦除实验，将其映射为双向斯特恩-盖拉赫框架，证明量子擦除是测量纠缠态的预期结果，逆因果性错觉源于不合法问题，时间正向描述即可解释该实验。
A coherence interpretation of nonlocal realism in the delayed-choice quantum eraser
本文用相干性解释延迟选择量子擦除器中类空间分离光子的非局域条纹，指出其源于符合探测引起的选择性测量和积基叠加，并强调固定和相位关系是传统粒子性量子力学无法解释的先决条件。
A realistic interpretation(REIN) of wave function in quantum mechanics is briefly presented in this work. In REIN, the wave function of a microscopic object is just its real existence rather than a mere mathematical description. Quantum object can exist in disjoint regions of space which just as the wave function distributes, travels at a finite speed, and collapses instantly upon a measurement. The single photon interference in a Mach-Zehnder interferometer is analyzed using REIN. In particular, we proposed and experimentally implemented a generalized delayed-choice experiment, the encounter-…
In this work we suggest a variant of the remarkable Wheeler's delayed choice gedanken experiment. In our experiment, single photon described by a superposition state with two terms dynamically interacts with an atom. Preparation of the atom in any of two excited states can be realized practically in the last moment before interaction. For atom in the first excited state there is practically none dynamical interaction between atom and photon so that the interference effects on the photon can be detected later by a photo plate. For atom in the second excited state dynamical interaction between p…
We describe an experimentally feasible protocol for performing a variant of the quantum delayed-choice experiment with massive objects. In this scheme, a single nitrogen-vacancy (NV) center in diamond driven by microwave fields is dispersively coupled to a massive mechanical resonator. A double-pulse Ramsey interferometer can be implemented with the spin-mechanical setup, where the second Ramsey microwave pulse drives the spin conditioned on the number states of the resonator. The probability for finding the NV center in definite spin states exhibits interference fringes when the mechanical re…
It was pointed out in the first part of this study that EPR-type entanglement is defined by the possibility of performing any of two mutually incompatible distant, i. e.,direct-interaction-free, measurements. They go together under the term 'EPR-type disentanglement'. In this second part, quantum-mechanical insight is gained in the real random delayed-choice erasure experiment of Kim et al. [Kim et al.: Phys. Rev. Lett. 84, 1-5 (2000)] by a relative-reality-of- unitarily-evolving-state (RRUES) approach (explained in the first part). Finally, it is shown that this remarkable experiment, which p…
Delayed Choice Phenomena in the Projection Evolution Model
本文探讨了光子通过马赫-曾德干涉仪的时间波函数轮廓，展示了延迟选择实验可通过干涉仪中光子与设备的时间重叠解释。
Motivated by the question, which kind of physical interactions and processes are needed for the production of quantum entanglement, Peres has put forward the radical idea of delayed-choice entanglement swapping. There, entanglement can be "produced a posteriori, after the entangled particles have been measured and may no longer exist". In this work we report the first realization of Peres' gedanken experiment. Using four photons, we can actively delay the choice of measurement-implemented via a high-speed tunable bipartite state analyzer and a quantum random number generator-on two of the phot…
Quantum entanglement is known as a unique feature of quantum mechanics, which cannot be obtained from classical physics. Recently, a coherence interpretation has been conducted for the delayed-choice quantum eraser using coherent photon pairs, where phase-locked symmetric frequency detuning between paired photons plays an essential role for selective measurement-caused nonlocal correlation. Here, a macroscopic version of the nonlocal correlation is presented using orthogonally polarized optical fields in a continuous wave quantum eraser scheme in a Mach-Zehnder interferometer (MZI). The result…
In a three-particle extension of Wheeler's delayed choice gedanken experiment, the quantum statistics of two particles is undetermined until a third particle is measured. As a function of the measurement result, the particles behave either as bosons or as fermions. The particles are distinguishable if no measurement is performed at all or when the measurement is performed in a rotated basis. The scheme is based on Greenberger-Horne-Zeilinger quantum correlations. It can be interpreted more generally as the encryption of maximally entangled states in a larger quantum superposition. The local qu…
Wave-particle duality has become one of the flagships of quantum mechanics. This counter-intuitive concept is highlighted in a delayed choice experiment, where the experimental setup that reveals either the particle or wave nature of a quantum system is decided after the system has entered the apparatus. Here we consider delayed choice experiments from the perspective of device-independent causal models and show their equivalence to a prepare-and-measure scenario. Within this framework, we consider Wheeler's original proposal and its variant using a quantum control and show that a simple class…
Delayed-choice erasure is investigated in two-photon two-slit experiments that are generalizations of the micromaser experiment of Scully et al. [Scully, M. O. et al. Nature 351, 111-116 (1991)]. Applying quantum mechanics to the localization detector, it is shown that erasure with delayed choice in the sense of Scully, has an analogous structure as simple erasure. The description goes beyond probabilities. The EPR-type disentanglement, consisting in two mutually incompatible distant measurements, is used as a general framework in both parts of this study. Two simple coherence cases are shown …
Nowadays the most intriguing features of wave particle complementarity of single photon is exemplified by the famous Wheeler's delayed choice experiment in linear optics, nuclear magnetic resonance and integrated photonic device systems. Studying the wave particle behavior in light and matter interaction at single photon level is challenging and interesting, which gives how single photons complement in light and matter interaction. Here, we demonstrate a Wheeler's delayed choice experiment in an interface of light and atomic memory, in which the cold atomic memory makes the heralded single pho…
Delayed Choice Lorentz Transformations on a Qubit
本文提出通过四维布洛赫球可视化持续监测的qubit状态，并利用洛伦兹变换描述其动力学，揭示延迟选择效应在量子测量中的表现。
Wave-particle duality has long been considered a fundamental signature of the non-classical behavior of quantum phenomena, specially in a delayed choice experiment (DCE), where the experimental setup revealing either the particle or wave nature of the system is decided after the system has entered the apparatus. However, as counter-intuitive as it might seem, usual DCEs do have a simple causal explanation. Here, we take a different route and under a natural assumption about the dimensionality of the system under test, we present an experimental proof of the non-classicality of a DCE based on t…
We consider a Wheeler delayed-choice experiment based on the Mach-Zehnder Interferometer. Since the development of the causal interpretation of relativistic boson fields there have not been any applications for which the equations of motion for the field have been solved explicitly. Here, we provide perhaps the first application of the causal interpretation of boson fields for which the equations of motion are solved. Specifically, we consider the electromagnetic field. Solving the equations of motion allows us to develop a relativistic causal model of the Wheeler delayed-choice Mach-Zehnder I…
Two observers (Alice and Bob) independently prepare two sets of singlets. They test one particle of each singlet along an arbitrarily chosen direction and send the other particle to a third observer, Eve. At a later time, Eve performs joint tests on pairs of particles (one from Alice and one from Bob). According to Eve's choice of test and to her results, Alice and Bob can sort into subsets the samples that they have already tested, and they can verify that each subset behaves as if it consisted of entangled pairs of distant particles, that have never communicated in the past, even indirectly …
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