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arXiv:1812.02346 · Physical Review A

Leggett-Garg macrorealism and the quantum nondisturbance conditions

Roope Uola, Giuseppe Vitagliano, Costantino Budroni

Published Oct 22, 2019• 37 citations
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Abstract

Macrorealism, the notion that macroscopic physical properties are well defined at all times and that it is possible to measure the properties without disturbing them, is tricky to test in an experiment, by admitting the ``clumsiness loophole.'' Here, a compatibility condition is found, so that a generalized version of macrorealism can hold for every initial state. This allows one to design stricter experimental tests of macrorealism for which an explanation in terms of ``clumsy'' measurements is harder to justify.

DOI
10.1103/physreva.100.042117

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Macrorealism, the notion that macroscopic physical properties are well defined at all times and that it is possible to measure the properties without disturbing them, is tricky to test in an experiment, by admitting the clumsiness loophole.'' Here, a compatibility condition is found, so that a generalized version of macrorealism can hold for every initial state. This allows one to design stricter experimental tests of macrorealism for which an explanation in terms of clumsy'' measurements is harder to justify.
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.
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.
Macrorealism is a classical world view asserting that the properties of macro-objects exist independently and irrespective of observation. One practical approach to test this view in quantum theory is to observe the quantum coherence for a macro-object in an interference experiment. An elegant and conceptually appealing approach for testing the notion of macrorealism in quantum theory is through the violation of Leggett-Garg inequality. However, a conclusive Leggett-Garg test hinges on how the noninvasive measurability criteria are guaranteed in an experiment and remains a debated issue to date. In this work, we connect the practical and the conceptual approaches for testing the macrorealism through the weak value. We argue that whenever a quantum effect is observed in an interference experiment there is an existence of anomalous weak value. Further, we demonstrate that whenever such weak value exists, one obtains the violation of a Leggett-Garg inequality in any interference experiment. Since in a path-only interference experiment effectively no prior measurement is performed, the Leggett-Garg test of macrorealism presented here is without assuming the noninvasive measurability. We provide a rigorous discussion about the assumptions involved in the Leggett-Garg scenario and how our scheme fits into it. Further, we provide a simple argument about the macrorealistic understanding of our results by using the recently developed approach involving quasiprobability.
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.
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.
Macrorealism formalizes the seemingly intuitive notion that, in contrast with the principles of quantum mechanics, a physical system can be in a definite state at any given time and moreover its dynamical evolution is independent of the measurements performed on it. In this study, we carry out a comparative analysis between three-time Leggett--Garg-type inequalities and the conditions of no-signaling-in-time and arrow-of-time for macrorealism within the context of meson oscillations. Our findings indicate that, under given initial conditions, no violations of Leggett--Garg inequalities are observed. However, no-signaling-in-time conditions are found to be violated, thereby revealing the impossibility of applying a macrorealistic description to the physics of meson oscillations.