Zheng-Hong Li, M. Al-Amri, M. Suhail Zubairy
We present an analysis of a double Mach-Zehnder interferometer in which an ensemble of identical pre- and postselected particles leave a weak trace. A knowledge of the weak value partially destroys the quantum interference. The results, contrary to some recent claims, are in accordance with the usual quantum mechanical expectations.
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Although there is no consensus regarding the "reality" of the past of a quantum particle, in situations where there is only one trajectory with nonvanishing quantum wave of the particle between its emission and detection points, it seems "safe" to associate the past of the particle with this trajectory. A method for analyzing the past of a quantum particle according to the weak trace it leaves is proposed. Such a trace can be observed via measurements performed on an ensemble of identically pre- and post-selected particles. Examples, in which this method contradicts the above common sense desc…
Comment on "Weak values and the past of a quantum particle"
本文反驳了Hance等人对弱值与量子粒子过去联系的批评，指出其结论源于对粒子过去方法的概念错误理解。
Vaidman, Phys.Rev. A 87, 052104 (2013), has proposed a weak value criterion for the past of a quantum particle, and applied it to photons in a particular setup of nested Mach-Zehnder interferometers. From his analysis, he draws some astonishing conclusions regarding which arms of the setup the photons populate. I argue that the weak values Vaidman employs as weak tracers in his analysis cannot be used in this case and that, consequently, the conclusions he draws cannot be upheld. The reason is that weak values are defined as a limit which in this case turns out to be discontinuous. I propose i…
The recent criticism of Vaidman's propsal for the analysis of the past of a particle in the nested interferometer is refuted. It is shown that the definition of the past of the particle adopted by Englert et al. [Phys. Rev. A 96, 022126 (2017)] is applicable only to a tiny fraction of photons in the interferometer which indeed exhibit different behaviour. Their proof that all pre- and postselected particles behave this way, i.e. follow a continuous trajectory, does not hold, because it relies on the assumption that it is intended to prove.
Vaidman has proposed a controversial criterion for determining the past of a single quantum particle based on the "weak trace" it leaves. We here consider more general examples of entangled systems and analyze the past of single, as well as pairs of entangled pre- and postselected particles. Systems with non-trivial time evolution are also analyzed. We argue that in these cases, examining only the single-particle weak trace provides information which is insufficient for understanding the system as a whole. We therefore suggest to examine, alongside with the past of single particles, also the p…
In a recent article [Chin. Phys. Lett. 34, 020301 (2017)], Ben-Israel et al. have claimed that the experiment proposed in [Chin. Phys. Lett. 32, 050303 (2015)] to determine the past of a quantum particle in a nested Mach-Zehnder interferometer does not work, and they have proposed a modification to the experiment. We show that their claim is false, and the modification is not required.
In a recent paper \cite{Matz}, Duprey and Matzin investigeated the meaning of vanishing "weak values" (WV), and their role in the retrodiction of the past of a pre- and post-selected quantum system in the presence of interference. Here we argue that any proposition, regarding the WV values, should be understood as a statement about the probability amplitudes, and revisit some of the conclusions reached in \cite{Matz}.
We stand by our findings in Phys. Rev A. 96, 022126 (2017). In addition to refuting the invalid objections raised by Peleg and Vaidman, we report a retrocausation problem inherent in Vaidman's definition of the past of a quantum particle.
Misinterpretation in the preceding Comment of my recent analysis of the past of a photon is corrected. There is nothing in this analysis which is "contrary to the usual quantum expectations" but, nevertheless, it does provide "further understanding and interpretation of the system considered". In particular, it teaches us that the naive common sense argument frequently used in the literature including the Comment has to be abandoned.
We discuss the preceding Comment and conclude that the arguments given there against the relevance of null weak values as representing the absence of a system property are not compelling. We give an example in which the transition matrix elements that make the projector weak values vanish are the same ones that suppress detector clicks in strong measurements. Whether weak values are taken to account for the past of a quantum system or not depend on general interpretional commitments of the quantum formalism itself rather than on peculiarities of the weak measurements framework.
Non-destructive weak measurements (WM) made on a quantum particle allow to extract information as the particle evolves from a prepared state to a finally detected state. The physical meaning of this information has been open to debate, particularly in view of the apparent discontinuous trajectories of the particle recorded by WM. In this work we investigate the properties of vanishing weak values for projection operators as well as general observables. We then analyze the implications when inferring the past of a quantum particle. We provide a novel (non-optical) example for which apparent dis…
Hashmi et al. [J. Phys. A 49, 345302 (2016)] claimed that the approach to the past of a quantum particle introduced by Vaidman [Phys. Rev. A 87, 052104 (2013)] has difficulties in certain examples and that it even can be refuted. Here I reply to their criticism showing that the approach provides a good explanation of all examples they considered. It is fully consistent with standard quantum mechanics and provides a useful tool for analyzing interference experiments.
In the paper "Does the weak trace show the past of a quantum particle?" [arXiv:2109.14060v2], it is argued that null weak values of the spatial projectors are inadequate to infer the presence of a quantum particle at an intermediate time between preparation and detection. This conclusion relies on two arguments - (i) the role of the disturbance induced by a weak measurement, and (ii) classical-like features like continuous paths that must purportedly be associated with a quantum particle presence. Here we first show that (i) arises from a misunderstanding of null weak values by putting forward…
Weak values inferred from weak measurements have been proposed as a tool to investigate trajectories of pre- and post-selected quantum systems. Are the inferences drawn from the weak values about the past of a quantum particle fully true? Can the two-state vector formalism predict everything that the standard formalism of quantum mechanics can? To investigate these questions we present a "which-path" gedanken experiment in which the information revealed by a pre- and post-selected quantum system is surprisingly different from what one would expect from the weak values computed using the two-st…
The question: "Where was a quantum particle between pre- and postselection measurements?" is analyzed in view of a recent proposal that it was in the overlap of the forward and backward evolving wave functions. It is argued that this proposal corresponds not only to the criterion of where the particle leaves a weak trace, but also where the local interactions can affect the probability of postselection and where finding the particle in a strong nondemolition measurement is possible. The concept of a "secondary presence" of a pre- and postselected particle where local interactions affect the we…
Following earlier applications of weak measurement to new cases (Part I), we proceed to explore its temporal peculiarities. We analyze an idealized experiment in which weak which-path measurements do not prevent consecutive weak interference effects, and then again the which-path information is recovered by strong measurements. We also show how the same effect can be obtained even by all these measurements being carried out on a single particle. The simplified setting enables critically assessing competing interpretations of the results. The most natural one is that of the Two-State-Vector For…
An ideal experiment is designed to determine the past of a particle in the nested Mach-Zehnder interferometer (MZI) by using standard quantum mechanics with quantum non-demolition measurements. We find that when the photon reaches the detector, it only follows one arm of the outer interferometer and leaves no trace in the inner MZI; while when it goes through the inner MZI, it cannot reach the detector. Our result obtained from the standard quantum mechanics is contradict to the statement based on two state vector formulism, "the photon did not enter the (inner) interferometer, the photon neve…
We analyze Vaidman's three-path interferometer with weak path marking [Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, "the particle's path" has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [Phys. Rev. Lett. …
Imaginary past of a quantum particle moving on imaginary time
通过解析延拓和绝热极限分析，研究量子粒子隧穿时间问题，发现透射粒子对历史记忆极少，表明该问题不适定。
We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32, 050303 (2015)] to the experiment of Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] does not test the past of the photon as characterised by local weak traces. Instead of answering the questions: (i) Were the photons in A? (ii) Were the photons in B? (iii) Were the photons in C? the proposed experiment measures a degenerate operator answering the questions: (i) Were the photons in A? (ii) Were the photons in B and C together? A negative answer to the last question does not tell us if photons were present in B or C. …
The nonlocal action of a measurement performed on a quantum entangled particle can determine the quantum state of a distant entangled particle instantly. Since the relativistic simultaneity of events is frame dependent therefore, a physically valid question arises, does the nonlocal action at a distance determine the quantum state of the distant particle in its past, when quantum state collapse is observed from a different inertial frame of reference? From the relativity of simultaneity, Lorentz invariance of the quantum entangled state of photons under consideration and the validity of Bell's…
In quantum physics, measurement results are random but their statistics can be predicted assuming some knowledge about the system in the past. Additional knowledge from a future measurement deeply changes the statistics in the present and leads to purely quantum features. In particular conditioned average outcomes of a weak measurement, so-called weak values, were shown to go beyond the conventional range, give a way to directly measure complex quantities, and can be used to enhance the sensitivity of quantum meters. Recently, these concepts have been considered in the general case of open qua…
We reexamine the thought experiment and real experiment of Vaidman et al., by placing Dove prisms in the nested Mach-Zehnder interferometer arms. In those previous works, the criterion of whether a single photon was present, or not, was the presence of a "weak trace", indicating the presence of a nonzero weak value. This was verified by slightly varying the mirror angle at a given frequency, which was then detected on a position sensitive detector at the oscillation frequency. We show the presence of the Dove prisms gives identical weak values everywhere to the previous configuration because t…
Weak values and the past of a quantum particle
本文批判用空间投影算符的非零弱值推断单个量子粒子历史路径的做法，指出测量扰动、经典存在观念误用、系综属性及未超越标准量子力学等四项根本问题。
An EPR experiment is studied where each particle within the entangled pair undergoes a few weak measurements (WMs) along some pre-set spin orientations, with the outcomes individually recorded. Then the particle undergoes one strong measurement along an orientation chosen at the last moment. Bell-inequality violation is expected between the two final measurements within each EPR pair. At the same time, statistical agreement is expected between these strong measurements and the earlier weak ones performed on that pair. A contradiction seemingly ensues: (i) Bell's theorem forbids spin values to …
We study the entanglement between two modes of Dirac field in an expanding spacetime characterized by the Robertson-Walker metric. This spacetime model turns out to be asymptotically (in the remote past and far future regions) Minkowskian. Then, on the one hand we show entanglement creation between particles and anti-particles when passing from remote past to far future. On the other hand we show that particles entanglement in the remote past degrades into the far future. These effects are traced back to particles creation. In our analysis we highlight the role of spin (polarization) of partic…
Weak measurement has enabled fundamental studies in both experiment and theory of quantum measurement. Numerous researches have indicated that weak measurements have a wide range of application and scientific research value. In our work, we used bibliometric methods to evaluate the global scientific output of research on Weak measurement and explore the current status and trends in this field from 2000 to 2020. The R bibliometric package was used for quantitative and qualitative analyses of publication outputs and author contributions. In total, 636 related articles and reviews were included i…
This chapter is based on a talk given at the Science and Ultimate Reality meeting in March, 2002, in honour of John Archibald Wheeler. In it, I discuss some questions related to what can and cannot be said about the history of a quantum mechanical system. Relying heavily on the weak- measurement formalism of Aharonov and coworkers, I argue that there is much to be learned about a system based both on its preparation and on subsequent postselection. This is illustrated with examples from a number of past, present, and future experiments from our lab, ranging from tests of quantum "paradoxes" to…
Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the p…
Quantum systems usually travel a multitude of different paths when evolving through time from an initial to a final state. In general, the possible paths will depend on the future and past boundary conditions, as well as the system's dynamics. We present a gedanken experiment where a single system apparently follows mutually exclusive paths simultaneously, each with probability one, depending on which measurement was performed. This experiment involves the measurement of observables that do not correspond to Hermitian operators. Our main result is a scheme for measuring these operators. The sc…
Reply to "Comment on `Weak values and the past of a quantum particle' ''
本文是对Vaidman评论的回复，指出其一方面承认仅是定义弱迹表征粒子存在，另一方面又用客观存在概念为该定义辩护，且该辩护循环依赖量子粒子位置总有确定事实的预设结论。
Monitoring a quantum observable continuously in time produces a stochastic measurement record that noisily tracks the observable. For a classical process such noise may be reduced to recover an average signal by minimizing the mean squared error between the noisy record and a smooth dynamical estimate. We show that for a monitored qubit this usual procedure returns unusual results. While the record seems centered on the expectation value of the observable during causal generation, examining the collected past record reveals that it better approximates a moving-mean Gaussian stochastic process …
In a recent paper, I argued against backward in time effects used by several authors to explain delayed choice experiments. I gave an explanation showing that there is no physical influence propagating from the present to the past and modifying the state of the system at a time previous to the measurement. However, though the solution is straightforward in the case of delayed choice experiments involving only one particle, it is subtler in the case of experiments involving two entangled particles because they give rise to EPR-like situations. Considering that a measurement is not an actual cha…
Griffiths [Phys. Rev. A 94, 032115 (2016)] analyzed, in the framework of consistent histories interpretation, the controversy regarding the approach to the past of a quantum particle introduced by Vaidman [Phys. Rev. A 87, 052104 (2013)]. I argue that Griffith's criticism of my approach using analysis of experiments with weak probes is unfounded.
We examine a recent argument that ``identical'' quantum particles with an anti-symmetric state (fermions) are weakly discernible objects, just like irreflexively related ordinary objects in situations with perfect symmetry (Black's spheres, for example). We conclude that the argument uses a silent premise that is not justified in the quantum case.
We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for quantum particles in a curved background space-time containing a spacelike singularity. As an example of such a metric we use the Schwarzschild metric, which contains two spacelike singularities, one in the past and one in the future. Since the particle world lines are everywhere timelike or lightlike, particles can be annihilated but not created at a future spacelike singularity, and created but not annihilated at a past spacelike singularity. It is argued that in the presence of future (past) spacelike singul…
An analysis of errors in measurement yields new insight into classically forbidden quantum processes. In addition to "physical" values, a realistic measurement can yield "unphysical" values; we show that in {\it sequences} of measurements, the "unphysical" values can form a consistent pattern. An experiment to isolate a particle in a classically forbidden region obtains a negative value for its kinetic energy. It is the {\it weak value} of kinetic energy between past and future state vectors.
Chaos and quantization of the three-particle generic Fermi-Pasta-Ulam-Tsingou model I: Density of states and spectral statistics
本文研究了三粒子 FPUT 模型的混合型经典动力学与量子对应物，推导了其简正模变换与半经典能量态密度，并验证了不同动力学区域下的能级统计规律，发现量子 Berry-Robnik 参数与经典值高度吻合。
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