Null weak values and the past of a quantum particle

Duprey, Q.; Matzkin, A.

doi:10.1103/physreva.95.032110

Cited by 33 publications

(48 citation statements)

References 32 publications

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“…Sec. II of [33]). 2 The imaginary part of A w is proportional to the shift of the momentum of the pointer wavefunctionfor a pointer in position space.…”

Section: B Weak Measurements and The Current Densitymentioning

confidence: 94%

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Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

2018

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We investigate the nonlocal dynamics of a single particle placed in an infinite well with moving walls. It is shown that in this situation, the Schrödinger equation (SE) violates local causality by causing instantaneous changes in the probability current everywhere inside the well. This violation is formalized by designing a gedanken faster-than-light communication device which uses an ensemble of long narrow cavities and weak measurements to resolve the weak value of the momentum far away from the movable wall. Our system is free from the usual features causing nonphysical violations of local causality when using the (nonrelativistic) SE, such as instantaneous changes in potentials or states involving arbitraily high energies or velocities. We explore in detail several possible artifacts that could account for the failure of the SE to respect local causality for systems involving time-dependent boundary conditions.

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“…Sec. II of [33]). 2 The imaginary part of A w is proportional to the shift of the momentum of the pointer wavefunctionfor a pointer in position space.…”

Section: B Weak Measurements and The Current Densitymentioning

confidence: 94%

“…Sec. II of [33] for a brief derivation) that the external pointer that was coupled to A has shifted by the quantity gA w where…”

Section: B Weak Measurements and The Current Densitymentioning

confidence: 99%

Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

2018

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“…In the general case, when both the pre and post-selected states are arbitrary, the real and imaginary parts of A w , given by Eqs. (21) and (22) Finally, we will argue below (Sec. IV F and IV G) that the system has no element of reality corresponding to A w .…”

Section: Weak Values As Generalized Eigenvalues In a Single Systemmentioning

confidence: 96%

“…It can hardly be maintained that the current density at a particular space-time point does not characterize a partial property of the system at that particular space-time point. We have amply discussed elsewhere [21,27] the case of null weak values. In the case of a projector A = |a k a k | , a null weak value A w = 0 means that the property represented by A cannot be registered by the weakly coupled pointer for the given post-selection.…”

Section: G the Meaning Of Weak Valuesmentioning

confidence: 99%

Weak Values and Quantum Properties

Matzkin

2019

Found Phys

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We investigate in this work the meaning of weak values through the prism of property ascription in quantum systems. Indeed, the weak measurements framework contains only ingredients of the standard quantum formalism, and as such weak measurements are from a technical point of view uncontroversial. However attempting to describe properties of quantum systems through weak values -the output of weak measurements -goes beyond the usual interpretation of quantum mechanics, that relies on eigenvalues. We first recall the usual form of property ascription, based on the eigenstate-eigenvalue link and the existence of "elements of reality". We then describe against this backdrop the different meanings that have been given to weak values. We finally argue that weak values can be related to a specific form of property ascription, weaker than the eigenvalues case but still relevant to a partial description of a quantum system.

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“…Such is, for example, the "three box paradox" [2]-[5], claiming that a particle can be, at the same time, at two different locations "with certainty". A similarly "paradoxical" suggestion that a photon could, on its way to detection, have visited the places it had "never entered, nor left, was made in [6]- [7], and further discussed in [8]- [11]. In the discussion of the Hardy's paradox [12]-[15] the particle is suspected of simultaneously "being and not being" at the same location [13].…”

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confidence: 99%

Path probabilities for consecutive measurements, and certain “quantum paradoxes”

Sokolovski

2018

Annals of Physics

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We consider a finite-dimensional quantum system, making a transition between known initial and final states. The outcomes of several accurate measurements, which could be made in the interim, define virtual paths, each endowed with a probability amplitude. If the measurements are actually made, the paths, which may now be called "real", acquire also the probabilities, related to the frequencies, with which a path is seen to be travelled in a series of identical trials. Different sets of measurements, made on the same system, can produce different, or incompatible, statistical ensembles, whose conflicting attributes may, although by no means should, appear "paradoxical". We describe in detail the ensembles, resulting from intermediate measurements of mutually commuting, or non-commuting, operators, in terms of the real paths produced. In the same manner, we analyse the Hardy's and the "three box" paradoxes, the photon's past in an interferometer, the "quantum Cheshire cat" experiment, as well as the closely related subject of "interaction-free measurements". It is shown that, in all these cases, inaccurate "weak measurements" produce no real paths, and yield only limited information about the virtual paths' probability amplitudes. PACS numbers:Recently, there has been significant interest in the properties of a pre-and post-selected quantum systems, and, in particular, in the description of such systems during the time between the preparation, and the arrival in the pre-determined final state (see, for example [1] and the Refs. therein). Intermediate state of the system can be probed by performing, one after another, measurements of various physical quantities. Although produced from the same quantum system, statistical ensembles, resulting from different sets of measurements, are known to have conflicting and seemingly incompatible qualities. These conflicts have, in turn, led to the discussion of certain "quantum paradoxes", allegedly specific to a system, subjected to post-selection. Such is, for example, the "three box paradox" [2]-[5], claiming that a particle can be, at the same time, at two different locations "with certainty". A similarly "paradoxical" suggestion that a photon could, on its way to detection, have visited the places it had "never entered, nor left, was made in [6]- [7], and further discussed in [8]- [11]. In the discussion of the Hardy's paradox [12]-[15] the particle is suspected of simultaneously "being and not being" at the same location [13]. The so called "quantum Cheshire cat" scheme [17]- [21] promises "disembodiment of physical properties from the object they belong to".One can easily dismiss a "paradox" of this type simply by noting that the conflicting features are never observed in the same experimental setup, and therefore, never occur "simultaneously" [5],[15], [22], [23], [24], [25] . (We agree: one can use a piece of plasticine to make a ball, or a cube, but should not claim that an object can be a ball and a cube at the same time.) There have been attempts to ascertain "simu...

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Null weak values and the past of a quantum particle

Cited by 33 publications

References 32 publications

Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

Nonlocality and local causality in the Schrödinger equation with time-dependent boundary conditions

Weak Values and Quantum Properties

Path probabilities for consecutive measurements, and certain “quantum paradoxes”

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