Observation and measurement of an optical Aharonov–Albert–Vaidman effect

Parks, Allen; Cullin, David W.; Stoudt, D.C.

doi:10.1098/rspa.1998.0288

Cited by 79 publications

(92 citation statements)

References 14 publications

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“…The relevance of (2.8) and (2.9) is that indeed the weight of a PPME measurement outcome distribution need not lie within the "normal" region of expectation defined by the bounds of the spectrum ofÂ ( Fig.1), contrary to what one would have naively expected given the generality of the spectral expansion of the PME distribution (2.3). This may not be obvious under strong measurement conditions, such that when the appartus wave function in p is expanded as a superposition of shifted wave functions 10) the overlap between two shifted functions φ(p − a) and φ(p − a ′ ) for all a = a ′ is negligible. Indeed, in such a case, the resulting p.d.f.…”

Section: Pre-and Postselected Measurement Statistics Eigenvaluesmentioning

confidence: 99%

“…The usefulness of this description has been demonstrated, both theoretically and experimentally, in a number of applications in which novel aspects of quantum processes have been uncovered when analyzed in terms of * Electronic address: abotero@uniandes.edu.co weak values. These include photon polarization interference [7,8,9,10,11], barrier tunnelling times [12,13,14], photon arrival times [15,16], anomalous pulse propagation [17,18,19], correlations in cavity QED experiments [20], complementarity in "which-way" experiments [21,22], non-classical aspects of light [23,24], communication protocols [25] and retrodiction "paradoxes" of quantum entanglement [26,27,28].…”

Section: Introductionmentioning

confidence: 99%

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Quantum averages of weak values

2005

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We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a definite mechanical effect on a measuring probe specifically designed to minimize the back-reaction on the measured system. We then present a new framework for general measurement conditions (where the back-reaction on the system may not be negligible) in which the measurement outcomes can still be interpreted as quantum averages of weak values. We show that in the classical limit, there is a direct correspondence between quantum averages of weak values and posterior expectation values of classical dynamical properties according to the classical inference framework.

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Section: Pre-and Postselected Measurement Statistics Eigenvaluesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum averages of weak values

2005

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“…A classical optical analog [6] of the original experiment proposed by AAV has been realized experimentally [7]. The polarization state of a classical radiation field can be treated as analogous to a spin-1 2 system, and the weak value of polarization may exceed the eigenvalue range [8,9]. It has also been found that weak values have applications within classical optical communication [10,11].…”

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confidence: 99%

Weak Measurements with Arbitrary Probe States

Johansen

2004

Phys. Rev. Lett.

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The exact conditions on valid pointer states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any pointer state with vanishing probability current density. This condition is found both for weak measurements of noncommuting observables and for c-number observables. In addition, the interaction between pointer and object must be sufficiently weak. There is no restriction on the purity of the pointer state. For example, a thermal pointer state is fully valid.PACS numbers: 03.65.Ta In "orthodox" quantum mechanics, the result of a "measurement" is always one of the eigenvalues of the observable. In the last pages of his textbook on quantum mechanics [1], von Neumann provided a model of a measurement where the object under study was interacting with a measurement pointer. By assuming that the initial uncertainty of the pointer was small, von Neumann demonstrated that the pointer would display one of the eigenvalues of the object observable.Aharonov, Albert and Vaidman (AAV) considered the same experimental arrangement [2]. However, they made the opposite assumption, namely that the initial uncertainty of the pointer was large. They demonstrated that despite this, the pointer would on average show the correct expectation value of an observableĉ, although it could not distinguish separate eigenvalues. Their most interesting discovery, though, was that if a projective measurement of a second observabled was made on the object after the interaction, the average meter reading conditioned on the result of the measurement on the object would be the real part of the quantityThe authors introduced the name "weak value" for this quantity. They observed that the values of c w might lie outside the range of eigenvalues of the observableĉ. It has been contested whether the experimental arrangement of AAV qualifies as a "measurement", and whether it has any meaning to ascribe to c w a significance as a "value" of the observableĉ [3][4][5]. Despite initial scepticism, weak values have found applications in a variety of systems. A classical optical analog [6] of the original experiment proposed by AAV has been realized experimentally [7]. The polarization state of a classical radiation field can be treated as analogous to a spin-1 2 system, and the weak value of polarization may exceed the eigenvalue range [8,9]. It has also been found that weak values have applications within classical optical communication [10,11]. These examples demonstrate * Electronic address: lars.m.johansen@hibu.no that weak values have applications beyond quantum mechanics. In fact, it is not unfamiliar that the quantum formalism can be applied even to classical systems where two observables cannot be jointly measured with arbitrary accuracy. This is known e.g. in signal processing, where the Wigner distribution for time and frequency has gained popularity [12].It was recently found that "weak values" have a deeper significance when considered from the viewpoint of standard Bayesian estimation theory [13]....

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“…While the interpretation of weak values remains somewhat controversial, several of the unusual properties predicted by weak value theory have been experimentally verified, e.g. [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

A Pointer Theory Explanation of Weak Value Persistence Occurring in the Quantum Three Box Experimental Data

Parks

Spence

2016

Acta Phys. Pol. A

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A concise exact pointer theory for von Neumann projector measurements of pre-and post-selected quantum systems has previously been used to formalize the notion of weak value persistence and apply it to explain pointer position data collected from a dynamical quantum non-locality detection experiment. This paper applies this exact pointer theory to provide an operational explanation of weak value persistence observed in the data obtained from a recent quantum box experiment.

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Observation and measurement of an optical Aharonov–Albert–Vaidman effect

Cited by 79 publications

References 14 publications

Quantum averages of weak values

Quantum averages of weak values

Weak Measurements with Arbitrary Probe States

A Pointer Theory Explanation of Weak Value Persistence Occurring in the Quantum Three Box Experimental Data

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