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Physical Review Letters

Proposed test for temporal Bell inequalities

Juan Pablo Paz, Günter Mahler A

Published Nov 15, 1993• 71 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.71.3235

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"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
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.
Previous work on Bell's inequality realized in the laboratory has used entangled photons. Here we describe how entangled atoms can violate Bell's inequality, and how these violations can be measured with a very high detection efficiency. We first discuss a simple scheme based on two-level atoms inside a cavity to prepare the entangled state. We then discuss a scheme using three-level atoms, which requires a parameter regime much easier to access experimentally using current technology. As opposed to other schemes, our proposal relies on the presence of finite decay rates and its implementation should therefore be much less demanding.
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.
"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."