Experimental violation of a Bell’s inequality in time with weak measurement

Palacios-Laloy, Agustin; Mallet, François; Nguyen, François; Bertet, Patrice; Vion, Denis; Estève, D.; Korotkov, Alexander N.

doi:10.1038/nphys1641

Cited by 362 publications

(433 citation statements)

References 32 publications

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“…of particle detectors or of avalanche processes, deserve to be studied through models. Measurements of a more elaborate type, in which some quantum property of S is continuously followed in time, are now being performed owing to experimental progress [307,308,361,362,319]. 152 In the Schrödinger picture, the expectation value of any (time-independent) observable for the subensemble E i was found from the stateD i of Eq.…”

Section: Other Types Of Measurementsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum-classical methods, to consistent histories and to modifications of the theory. Next, a flexible and rather realistic quantum model is introduced, describing the measurement of the z-component of a spin through interaction with a magnetic memory simulated by a Curie-Weiss magnet, including N 1 spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out, exhibiting several time scales. Conditions on the parameters of the model are found, which ensure that the process satisfies all the features of ideal measurements. Various imperfections of the measurement are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrixD(t). Its off-diagonal blocks in a basis selected by the spin-pointer coupling, rapidly decay owing to the many degrees of freedom of the pointer. Recurrences are ruled out either by some randomness of that coupling, or by the interaction with the bath. On a longer time scale, the trend towards equilibrium of the magnet produces a final stateD(t f ) that involves correlations between the system and the indications of the pointer, thus ensuring registration. AlthoughD(t f ) has the form expected for ideal measurements, it only describes a large set of runs. Individual runs are approached by analyzing the final states associated with all possible subensembles of runs, within a specified version of the statistical interpretation. There the difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrixD(t f ) into a sum of sub-matrices, so that one cannot infer from its sole determination the states that would describe small subsets of runs. This difficulty is overcome by dynamics due to suitable interactions within the apparatus, which produce a special combination of relaxation and decoherence associated with the broken invariance of the pointer. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory; the reduction of the state for each individual run follows. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run and the emergence of classicality in a measurement process. Finally, pedagogical exercises are proposed and lessons for future works on m...

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Section: Other Types Of Measurementsmentioning

confidence: 99%

Understanding quantum measurement from the solution of dynamical models

Allahverdyan¹,

Balian²,

2013

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“…Violations of the Leggett-Garg inequalities under decoherence were experimentally studied in Refs. [11,12].…”

Section: Introductionmentioning

confidence: 99%

On generalized entropies and information-theoretic Bell inequalities under decoherence

Rastegin

2015

Annals of Physics

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We consider information-theoretic inequalities of the Bell type in the presence of decoherence. It is natural that too strong coupling with the environment can prevent an observation of quantum correlations. In this regard, the use of various entropic functions may give additional capabilities to reveal desired correlations. It was already shown that the Bell and Leggett-Garg inequalities in terms conditional Tsallis entropies are more sensitive in the cases of detection inefficiencies. In this paper, we study capabilities of generalized conditional entropies of the Tsallis type in analyzing the Bell theorem in decoherence scenarios. Two forms of the conditional Tsallis q-entropy are known in the literature. We show that each of them can be used for defining a metric in the probability space of interest. Such metrics can be used in realizing the so-called triangle principle. The triangle principle has recently been proposed as a unifying approach to questions of local realism and noncontextuality. Applying the triangle principle leads to the two families of q-metric inequalities of the Bell type. Information-theoretic formulations in terms of the q-entropic metrics are first discussed for the CHSH scenario in dephasing environment. Then we also revisit q-entropic inequalities of the Leggett-Garg type. An environmental influence is modeled by the phase damping channel and by the depolarizing channel.

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“…The use of the technique for amplification purposes has been spectacular [7][8][9]. Weak measurements have also been employed to illuminate the fundamental difference between classical and quantum mechanics exhibited by violation of Leggett-Garg inequalities [3,[10][11][12][13][14], also called "Bell inequalities in time".…”

Section: Introductionmentioning

confidence: 99%

“…Note that I do not here question the weak value as a measureable entity pertaining to the system under study, nor the many ingenious ways experimentalist have exploited the weak measurement + post-selection idea ( [5][6][7][8][9][11][12][13][14]; see also [3] for a brief review). What I do question is whether a weak value can be given an 'ordinary' meaning.…”

Section: Introductionmentioning

confidence: 99%

What Is a Quantum-Mechanical “Weak Value” the Value of?

Svensson

2013

Found Phys

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A so called "weak value" of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three-Box Paradox and Hardy's Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations.

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Experimental violation of a Bell’s inequality in time with weak measurement

Cited by 362 publications

References 32 publications

Understanding quantum measurement from the solution of dynamical models

Understanding quantum measurement from the solution of dynamical models

On generalized entropies and information-theoretic Bell inequalities under decoherence

What Is a Quantum-Mechanical “Weak Value” the Value of?

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