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AIP conference proceedings

The Retrocausal Nature of Quantum Measurement Revealed by Partial and Weak Measurements

Avshalom C. Elitzur, Eliahu Cohen, Daniel P. Sheehan

Published Jan 1, 2011• 15 citations
Publisher

Abstract

Quantum measurement is sometimes more effective when its result is not definite. Partial measurement turns the initial superposition not into a certain state but to a greater probability for it, enabling probing the quantum state in cases where complete measurement makes the noncommuting variables inaccessible. It also enables full quantum erasure that, unlike prevailing method, can be carried out even on recorded results. Aharonov's weak measurement is another method of imprecisely measuring quantum variables, outsmarting the uncertainty principle in even subtler ways. Happily, the two methods complement and corroborate one another in several interesting ways. We gedankenly apply these measurements to the EPR case. A pair of entangled particles undergoes more than one pair of partial and weak measurements, which, unlike complete measurements, leave them partially correlated. Their erasure is then shown to be as nonlocal as measurement itself. Surprisingly, the temporal relations between such measurements in the EPR setting do not follow the temporal sequence perceived by an external observer. For each particle, the measurements performed on the other operate as if they occurred (with signs reversed) in its own past, and in reversed order. This fully accords with Cramer's transactional interpretation and Aharonov's two state‐vector formalism.

DOI
10.1063/1.3663720

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One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.

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Quantum measurement is sometimes more effective when its result is not definite. Partial measurement turns the initial superposition not into a certain state but to a greater probability for it, enabling probing the quantum state in cases where complete measurement makes the noncommuting variables inaccessible. It also enables full quantum erasure that, unlike prevailing method, can be carried out even on recorded results. Aharonov's weak measurement is another method of imprecisely measuring quantum variables, outsmarting the uncertainty principle in even subtler ways. Happily, the two methods complement and corroborate one another in several interesting ways. We gedankenly apply these measurements to the EPR case. A pair of entangled particles undergoes more than one pair of partial and weak measurements, which, unlike complete measurements, leave them partially correlated. Their erasure is then shown to be as nonlocal as measurement itself. Surprisingly, the temporal relations between such measurements in the EPR setting do not follow the temporal sequence perceived by an external observer. For each particle, the measurements performed on the other operate as if they occurred (with signs reversed) in its own past, and in reversed order. This fully accords with Cramer's transactional interpretation and Aharonov's two state‐vector formalism.
Partial measurement turns the initial superposition not into a definite outcome but into a greater probability for it. The probability can approach 100%, yet the measurement can undergo complete quantum erasure. In the Einstein-Podolsky-Rosen (EPR) setting, we prove that (i) every partial measurement nonlocally creates the same partial change in the distant particle, and (ii) every erasure inflicts the same erasure on the distant particle's state. This enables an EPR experiment where the nonlocal effect does not vanish after a single measurement but keeps ``traveling'' back and forth between particles. We study an experiment in which two distant particles are subjected to interferometry with a partial ``which path'' measurement. Such a measurement causes a variable amount of correlation between the particles. A new inequality is formulated for same-angle polarizations, extending Bell's inequality for different angles. The resulting nonlocality proof is highly visualizable, as it rests entirely on the interference effect. Partial measurement also gives rise to a new form of entanglement, where the particles manifest correlations of multiple polarization directions. Another novelty in that the measurement to be erased is fully observable, in contrast to prevailing erasure techniques in which it can never be observed. Some profound conceptual implications of our experiment are briefly pointed out.
Quantum weak measurement is presented as shedding new light on the retrocausality question. It is shown to leave a system almost unaffected while gathering information about it. Next, an EPR experiment is studied where each particle undergoes a few weak measurements along some pre-set spin orientations. These weak outcomes are individually recorded. Then the particle undergoes a strong measurement along a spin orientation freely chosen at the last moment. Bell-inequality violation is expected between the two final strong measurements within each EPR pair. At the same time, agreement is expected between these strong measurements and the earlier weak ones performed on that pair. A contradiction thereby ensues: i) Bell’s theorem forbids spin values to exist prior to the choice of the spin-orientation to be measured; ii) A weak measurement cannot determine the outcome of a successive strong one; and iii) Indeed no disentanglement is inflicted by the weak measurements; yet iv) The weak measurements’ outcomes agree with those of the strong ones, suggesting the existence of pre-determined values. The most reasonable resolution seems to be that of the Two-State-Vector Formalism, namely, that the experimenter’s choice has been encrypted within the weak measurement’s outcomes, even before the experimenter themselves knows what their choice will be. Causal loops are avoided by this anticipation remaining encrypted until the final outcomes enable to decipher it.
Entanglement and nonlocality are studied in the framework of pre-/postselected ensembles with the aid of weak measurements and the two-state-vector formalism. In addition to the EPR–Bohm experiment, we revisit the Hardy and Cheshire Cat experiments, whose entangled pre- or postselected states give rise to curious phenomena. We then turn to even more peculiar phenomenon suggesting “emerging correlations” between independent preand postselected ensembles of particles. This can be viewed as a quantum violation of the classical “pigeonhole principle.” Introduction It is seldom acknowledged that seven years before the celebrated Bell paper [1], Bohm and Aharonov [2] published an analysis of the EPR paradox [3]. They suggested an experimental setup, based on Compton scattering, for testing nonlocal correlations between the polarizations of two annihilation photons. In 1964, Bell proposed his general inequality, thereby excluding local realism. During the same time, Aharonov et al. constructed the foundations of a time-symmetric formalism of quantum mechanics [4]. While Bell's proof utilizes entanglement to demonstrate nonlocal correlations,wewill describe inwhat follows the emergence of nonlocal correlations between product states. For this purpose, however, we shall invoke weak measurements of pre- and postselected ensembles. In classical mechanics, initial conditions of position and velocity for every particle fully determine the time evolution of the system. Therefore, trying to impose an additional final condition would lead either to redundancy or to inconsistency with the initial conditions. This is radically different in quantum mechanics. Because of the uncertainty principle, an initial state vector does not fully determine, in general, the outcome of a future measurement. However, adding a final (backward-evolving) state vector results in a more complete description of the quantum system in between these two boundary conditions, which has a bearing on the determination of measurement outcomes. The basis for this time-symmetric formulation of quantum mechanics was laid down by Aharonov, Bergman, and Lebowitz (ABL), who derived a symmetric probability rule concerning measurements performed on systems, while taking into account the final state of the system, in addition to the usual initial state [4].
We analyze an idealized experiment in which weak which-path measurements do not prevent consecutive weak interference measurements, 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 strong and weak measurements being carried out on a single particle. The simplified setting enables critically assessing competing interpretations of the results. The most natural one turns out to be that of the Two-State-Vector Formalism, according to which the quantum two-state between an earlier and a later measurement is equally determined by both of them.
We argue that the conclusion of Bell theorem, namely, that there must be spatial non-local correlations in certain experimental situations, does not apply to typical individual measurements performed on entangled EPR pairs. Our claim is based on three points, (i) on the notion of quantum {\it complete measurements}; (ii) on Bell results on local yet distant measurements; and (iii) on the fact that perfect simultaneity is banned by the quantum mechanics. We show that quantum mechanics indicates that, while the measurements of the pair members are indeed space-like separated, the pair measurement is actually a sequence of two complete measurements, the first one terminating the entanglement and, therefore, the second one becoming unrelated to the initial preparation of the entangled pair. The outstanding feature of these measurements is that neither of them violates the principle of locality. We discuss that the present measurement viewpoint appears to run contrary to the usual interpretation of "superposition" of states with its concomitant "collapse" on measurement.
One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.