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arXiv:1901.06183

Proposal for a loophole-free test of macroscopic realism

Devashish Pandey, Xavier Oriols, Guillermo Albareda

Published Jan 18, 2019• 0 citations
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Abstract

We propose a test of macrorealism that exploits the contextuality of two-time correlation functions to escape the so-called clumsiness loophole that plagues Leggett-Garg inequalities. The non-contextuality of reduced joint probability distributions is proven to be an unequivocal criterion to guarantee that measurements are carried out in the ideally-weak measurement regime of a class of generalized von Neumann measurements. In this regime, testing the so-called no-signaling in time condition allows to uncontextually ascertain whether a property of a given system is macrorealistic or non-macrorealistic. The resulting protocol allows for tests of macrorealism in situations where Leggett-Garg inequalities and ideal negative measurement cannot be used at all.

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We propose a test of macrorealism that exploits the contextuality of two-time correlation functions to escape the so-called clumsiness loophole that plagues Leggett-Garg inequalities. The non-contextuality of reduced joint probability distributions is proven to be an unequivocal criterion to guarantee that measurements are carried out in the ideally-weak measurement regime of a class of generalized von Neumann measurements. In this regime, testing the so-called no-signaling in time condition allows to uncontextually ascertain whether a property of a given system is macrorealistic or non-macrorealistic. The resulting protocol allows for tests of macrorealism in situations where Leggett-Garg inequalities and ideal negative measurement cannot be used at all.
The rise of quantum information theory has lent new relevance to experimental tests for non-classicality, particularly in controversial cases such as adiabatic quantum computing superconducting circuits. The Leggett-Garg inequality is a "Bell inequality in time" designed to indicate whether a single quantum system behaves in a macrorealistic fashion. Unfortunately, a violation of the inequality can only show that the system is either (i) non-macrorealistic or (ii) macrorealistic but subjected to a measurement technique that happens to disturb the system. The "clumsiness" loophole (ii) provides reliable refuge for the stubborn macrorealist, who can invoke it to brand recent experimental and theoretical work on the Leggett-Garg test inconclusive. Here, we present a revised Leggett-Garg protocol that permits one to conclude that a system is either (i) non-macrorealistic or (ii) macrorealistic but with the property that two seemingly non-invasive measurements can somehow collude and strongly disturb the system. By providing an explicit check of the invasiveness of the measurements, the protocol replaces the clumsiness loophole with a significantly smaller "collusion" loophole. © 2011 Springer Science+Business Media, LLC.
Abstract We propose a protocol that allows to assess the precise correspondence between thought and practical experiments, a critical point for addressing experimental clumsiness in a test of macro- or micro-realism. Two-time generalized von Neumann measurements of properties <?CDATA A\mathcal{A}A?> A and <?CDATA B\mathcal{B}B?> B are shown to obey the so-called no-signaling in time condition for initial states defined as an incoherent sum of eigenstates of <?CDATA A\mathcal{A}A?> A . An experiment for witnessing the use of this type of measurements in the laboratory is then devised by proving the existence of five conditions that have to be fulfilled by any generalized von Neumann measurement. Ensuring the use of this type of measurements and then testing the no-signaling in time condition for a range of system-meter coupling strengths allows to test realism in a highly reproducible manner and to critically narrow the so-called clumsiness loophole. The resulting protocol is applicable to general (not only dichotomic) variables, and it is employed to show, both analytically for general systems and numerically for a collection of harmonic oscillators, that quantum systems made of a large number of uncorrelated particles are genuinely macrorealist, i.e., realistic with respect to all intensive properties at any time.
In 1985, Leggett and Garg put forward the concept of macroscopic realism (macrorealism) and, in analogy to Bell's theorem, derived a necessary condition in terms of inequalities, which are now known as the Leggett-Garg inequalities. In this paper, we discuss another necessary condition called no-signaling in time. It solely bases on comparing the probability distribution for a macrovariable at some time for the cases where previously a measurement has or has not been performed. Although the concept is analogous to the no-signaling condition in the case of Bell tests, it can be violated according to quantum mechanical predictions even in situations where no violation of Leggett-Garg inequalities is possible.
In the tests for macrorealism proposed by Leggett and Garg, the temporal correlation functions of a dichotomic variable QQQ must be measured in a noninvasive way to rule out alternative classical explanations of Leggett-Garg inequality violations. Ideal negative measurements in which a null result is argued to be a noninvasive determination of the system's state are often used. From a quantum-mechanical perspective, such a measurement collapses the wave function and will therefore typically be found to be invasive under any experimental check. Here, a simple modified ideal negative measurement protocol is described for measuring the correlation functions, which is argued to be noninvasive from both classical and quantum perspectives and hence the noninvasiveness can then be checked experimentally, thereby permitting a quantitative measure of the degree of clumsiness of the measurement. It is also shown how this procedure may be extended to measure higher-order correlation functions, and a number of higher-order conditions for macrorealism are derived.
The Leggett-Garg inequality holds for any macrorealistic system that is being measured noninvasively. A violation of the inequality can signal that a system does not conform to our primal intuition about the physical world. Alternatively, a violation can simply indicate that a ``clumsy'' experimental technique led to invasive measurements. Here, we consider a recent Leggett-Garg test designed to try to rule out the mundane second possibility. We tailor this Leggett-Garg test to the IBM 5Q Quantum Experience system and find compelling evidence that qubit Q2{Q}_{2}Q2​ of the system cannot be described by noninvasive macrorealism.
Abstract The Leggett-Garg (LG) inequalities were introduced, as a temporal parallel of the Bell inequalities, to test macroscopic realism – the view that a macroscopic system evolving in time possesses definite properties which can be determined without disturbing the future or past state. The original LG inequalities are only a necessary condition for macrorealism, and are therefore not a decisive test. We argue, for the case of measurements of a single dichotomic variable Q, that when the original four three-time LG inequalities are augmented with a set of twelve two-time inequalities also of the LG form, Fine’s theorem applies and these augmented conditions are then both necessary and sufficient. A comparison is carried out with the alternative necessary and sufficient conditions for macrorealism based on no-signaling in time conditions which ensure that all probabilities for Q at one and two times are independent of whether earlier or intermediate measurements are made. We argue that the two tests differ in their implementation of the key requirement of non-invasive measurability so are testing different notions of macrorealism, and these notions are elucidated.