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Are violations to temporal Bell inequalities there when somebody looks?

Tommaso Calarco, Michele Cini, Roberto Onofrio

Published Aug 10, 1999• 11 citations
OpenAlex

Abstract

The possibility of observing violations of temporal Bell inequalities, originally proposed by Leggett as a mean of testing the quantum mechanical delocalization of suitably chosen macroscopic bodies, is discussed by taking into account the effect of the measurement process. A general criterion quantifying this possibility is defined and shown not to be fulfilled by the various experimental configurations proposed so far to test inequalities of different forms.

Related papers

Are violations to temporal Bell inequalities there when somebody looks?

T Calarco, M Cini, Roberto Onofrio

The possibility of observing violations of temporal Bell inequalities, originally proposed by Leggett and Garg as a mean of testing the quantum-mechanical delocalization of suitably chosen macroscopic bodies, is discussed by taking into account the effect of the measurement process. A general criterion quantifying this possibility is defined and shown not to be fulfilled by the various experimental configurations proposed so far to test inequalities of different forms.

arXiv:quant-ph/9908030•Europhysics Letters (EPL)•Aug 15, 1999•10 citations

Some theoretical considerations related to the experimental tests of a Temporal Bell's inequality

Mao-Chuang Yeh

"According to the quantum superposition principle, quantum mechanics at the macroscopic scale predicts that a macroscopic system can be in more than one distinct state at the same time. Such an extrapolation of quantum mechanics contradicts our everyday instinct, summarized by Leggett and Garg (LG) under the heading of macrorealism (MR) [1]. To resolve the conflict and to determine whether MR or quantum mechanics is the right description of macroscopic objects, in 1985, Leggett and Garg [1] proposed the temporal Bell's inequality (TBI). If a macorealist description is possible, the inequality is satisfied - quantum mechanics, on the other hand, predicts a violation. Thereafter, people were motivated to engineer macroscopic quantum systems and to test the TBI. In the TBI, one of the most critical postulates is that of the noninvasive measurability (NIM) : it is in principle possible to determine which state the system is in with an arbitrarily small e ect on the subsequent system dynamics. To satisfy the NIM postulate in the TBI experiment, the implementation of the ""ideal negative result"" (INR) measurement was also proposed by LG [1]. In a two-state system, an INR measurement is designed to interact (in each run) with only one of two system states. Only runs where the measurement reported no outcome are kept. Although in the last few years there have been tests of the TBI on microscopic systems with the use of INR measurements [4] and on macroscopic systems using weak measurement [5], no one has ever implemented INR measurements on macroscopic systems in TBI tests so far. In addition, the NIM postulate was simply assumed, and not veri ed by an ancillary test [9, 3]. With these considerations in mind, there are two main tasks in this thesis: the rst one is to analyze the realization of an INR measurement on a macroscopic object. I propose an experiment based on coupling a flux-qubit to a dcSQUID, which mirrors the approach of Knee et al. [4], where the system of interest is coupled to another quantum system which acts as a measuring device. In order to accomplish the first task, we analyze the escape dynamics of a flux-qubit SQUID composite system in various limits and discuss the prospects of operating in a regime realizing a von Neumann (""projective"")-like measurement onto the qubit flux basis. Later in the thesis, I discuss current feasibility of the proposed experiment based on the possible measurement error (the ""venality"" [4]) of our INR measurement. The second task is to analyze experimental tests of measurement invasiveness. I propose a concrete protocol, ancillary to the main TBI experiment, which may narrow some loopholes in the test of MR [3]. I generalize the approach of Wilde and Mizel [3], using the behavior of the two-time correlator of a system as an indicator of measurement invasiveness. The measured invasivities can be used to give a improved lower bound for the TBI."

•Aug 16, 2016•1 citation

Proposed test for temporal Bell inequalities

Juan Pablo Paz, Günter Mahler A

Temporal Bell inequalities can be violated for sequences of events (histories) for which probabilities satisfying consistent sum rules cannot be defined. We discuss possible experiments in which such violations, never observed so far, may indeed be seen. The basic scheme, which uses three optically driven and mutually interacting two-level systems, could be implemented in a variety of nanostructures. It could even be mapped onto the dynamics of a single electron four-level system thus allowing for a realization in atomic physics.

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Realism with Quantum Faces: The Leggett–Garg Inequalities as a Case Study for Feyerabend's Views

Elise M. Crull

In this paper I attempt to broaden Feyerabend scholarship by asking whether and how Feyerabend's philosophy of science, in particular his commitments to realism and pluralism about scientific theories as well as anarchism about scientific methods, is borne out in multidisciplinary research concerning the Leggett–Garg inequalities. These inequalities were derived explicitly to be a temporal analogue to Bell's inequalities: the viability of macroscopic realism is tested against the predictions of quantum mechanics by performing a series measurements on a macroscopic variable of one system at different time intervals, then evaluating correlations among resultant values. In the nearly forty years since Leggett and Garg's paper, questions continue to be raised whether common tests of these inequalities reveal genuine violations or merely experimental disturbances. There is also much debate about what genuine violations in fact signify, if (as most agree) they are not straight-forwardly analogous to Bell tests. Taking this fascinating and as yet largely unsettled episode from physics as a case study, I derive three Feyerabendian lessons that demonstrate the relevance of his views even today.

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Contra Classical Causality Violating Temporal Bell Inequalities in Mental Systems

Harald Atmanspacher A, Thomas Filk A

Temporally non-local measurements – single measurements yielding information about the state of a system at different instances – may provide a way to observe non-classical behavior in mental systems. The signature for such behavior is a violation of temporal Bell inequalities. We present such inequalities applicable to scenarios with two alternating mental states, such as in the perception of ambiguous figures. We indicate empirical options for testing temporal Bell inequalities, and speculate about possible explanations in case these inequalities are indeed violated.

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Temporal Bell inequalities without noninvasive measurability

Ramón Lapiedra

Some temporal Bell inequalities are deduced under the assumption of realism and perfect correlation. No locality condition is needed. When the system is macroscopic, the perfect correlation assumption substitutes the noninvasive measurability hypothesis advanteousgely. The new inequalities are violated quantically. This violation is clearly more severe than the similar violation in the case of ordinary Bell inequalities. Some microscopic and macroscopic situations in which these inequalities could be tested are considered.

arXiv:quant-ph/0502052•Feb 9, 2005•0 citations
The possibility of observing violations of temporal Bell inequalities, originally proposed by Leggett as a mean of testing the quantum mechanical delocalization of suitably chosen macroscopic bodies, is discussed by taking into account the effect of the measurement process. A general criterion quantifying this possibility is defined and shown not to be fulfilled by the various experimental configurations proposed so far to test inequalities of different forms.
"According to the quantum superposition principle, quantum mechanics at the macroscopic scale predicts that a macroscopic system can be in more than one distinct state at the same time. Such an extrapolation of quantum mechanics contradicts our everyday instinct, summarized by Leggett and Garg (LG) under the heading of macrorealism (MR) [1]. To resolve the conflict and to determine whether MR or quantum mechanics is the right description of macroscopic objects, in 1985, Leggett and Garg [1] proposed the temporal Bell's inequality (TBI). If a macorealist description is possible, the inequality is satisfied - quantum mechanics, on the other hand, predicts a violation. Thereafter, people were motivated to engineer macroscopic quantum systems and to test the TBI. In the TBI, one of the most critical postulates is that of the noninvasive measurability (NIM) : it is in principle possible to determine which state the system is in with an arbitrarily small e ect on the subsequent system dynamics. To satisfy the NIM postulate in the TBI experiment, the implementation of the ""ideal negative result"" (INR) measurement was also proposed by LG [1]. In a two-state system, an INR measurement is designed to interact (in each run) with only one of two system states. Only runs where the measurement reported no outcome are kept. Although in the last few years there have been tests of the TBI on microscopic systems with the use of INR measurements [4] and on macroscopic systems using weak measurement [5], no one has ever implemented INR measurements on macroscopic systems in TBI tests so far. In addition, the NIM postulate was simply assumed, and not veri ed by an ancillary test [9, 3]. With these considerations in mind, there are two main tasks in this thesis: the rst one is to analyze the realization of an INR measurement on a macroscopic object. I propose an experiment based on coupling a flux-qubit to a dcSQUID, which mirrors the approach of Knee et al. [4], where the system of interest is coupled to another quantum system which acts as a measuring device. In order to accomplish the first task, we analyze the escape dynamics of a flux-qubit SQUID composite system in various limits and discuss the prospects of operating in a regime realizing a von Neumann (""projective"")-like measurement onto the qubit flux basis. Later in the thesis, I discuss current feasibility of the proposed experiment based on the possible measurement error (the ""venality"" [4]) of our INR measurement. The second task is to analyze experimental tests of measurement invasiveness. I propose a concrete protocol, ancillary to the main TBI experiment, which may narrow some loopholes in the test of MR [3]. I generalize the approach of Wilde and Mizel [3], using the behavior of the two-time correlator of a system as an indicator of measurement invasiveness. The measured invasivities can be used to give a improved lower bound for the TBI."
Temporal Bell inequalities can be violated for sequences of events (histories) for which probabilities satisfying consistent sum rules cannot be defined. We discuss possible experiments in which such violations, never observed so far, may indeed be seen. The basic scheme, which uses three optically driven and mutually interacting two-level systems, could be implemented in a variety of nanostructures. It could even be mapped onto the dynamics of a single electron four-level system thus allowing for a realization in atomic physics.
In this paper I attempt to broaden Feyerabend scholarship by asking whether and how Feyerabend's philosophy of science, in particular his commitments to realism and pluralism about scientific theories as well as anarchism about scientific methods, is borne out in multidisciplinary research concerning the Leggett–Garg inequalities. These inequalities were derived explicitly to be a temporal analogue to Bell's inequalities: the viability of macroscopic realism is tested against the predictions of quantum mechanics by performing a series measurements on a macroscopic variable of one system at different time intervals, then evaluating correlations among resultant values. In the nearly forty years since Leggett and Garg's paper, questions continue to be raised whether common tests of these inequalities reveal genuine violations or merely experimental disturbances. There is also much debate about what genuine violations in fact signify, if (as most agree) they are not straight-forwardly analogous to Bell tests. Taking this fascinating and as yet largely unsettled episode from physics as a case study, I derive three Feyerabendian lessons that demonstrate the relevance of his views even today.
Temporally non-local measurements – single measurements yielding information about the state of a system at different instances – may provide a way to observe non-classical behavior in mental systems. The signature for such behavior is a violation of temporal Bell inequalities. We present such inequalities applicable to scenarios with two alternating mental states, such as in the perception of ambiguous figures. We indicate empirical options for testing temporal Bell inequalities, and speculate about possible explanations in case these inequalities are indeed violated.
Some temporal Bell inequalities are deduced under the assumption of realism and perfect correlation. No locality condition is needed. When the system is macroscopic, the perfect correlation assumption substitutes the noninvasive measurability hypothesis advanteousgely. The new inequalities are violated quantically. This violation is clearly more severe than the similar violation in the case of ordinary Bell inequalities. Some microscopic and macroscopic situations in which these inequalities could be tested are considered.