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arXiv:quant-ph/0009016 · Physical Review A

Violations of Bell inequalities for measurements with macroscopic uncertainties: What it means to violate macroscopic local realism

M. D. Reid

Published Jul 18, 2000• 14 citations
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Abstract

We suggest a method to test the premise of ``macroscopic local realism'' that is sufficient to derive Bell inequalities when measurements of photon numbers are only accurate to an uncertainty of order n photons, where n is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy ``elements of reality'' that have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of macroscopic local realism. Quantum states violating this macroscopic local realism are presented.

DOI
10.1103/physreva.62.022110

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We suggest a method to test the premise of macroscopic local realism'' that is sufficient to derive Bell inequalities when measurements of photon numbers are only accurate to an uncertainty of order n photons, where n is macroscopic. Macroscopic local realism is only sufficient to imply, in the context of the original Einstein-Podolsky-Rosen argument, fuzzy elements of reality'' that have a macroscopic indeterminacy. We show therefore how the violation of local realism in the presence of macroscopic uncertainties implies the failure of macroscopic local realism. Quantum states violating this macroscopic local realism are presented.
We consider a new version of the Einstein - Podolsky - Rosen (EPR) paradox in which the measurements have limited accuracy, so that a photon number is specified only to plus or minus a macroscopic number of photons. In our example the minimum quantum uncertainty product for the two relevant conjugate quantities is itself a macroscopic photon number. This new version of the EPR situation is stronger than the original microscopic versions, which were based on the validity, now disproved by Bell experiments, of `local realism' at a microscopic level. The new version is based on the validity of `macroscopic local realism', which has to date not been questioned.
We show that quantum mechanics predicts an Einstein-Podolsky-Rosen paradox (EPR), and also a contradiction with local hidden variable theories, for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new, very strong premise, called macroscopic local realism. We link this premise to the Schrodinger-cat paradox. Our proposed experiments ensure all fields incident on each measurement apparatus are macroscopic. We show that an alternative measurement scheme corresponds to balanced homodyne detection of quadrature phase amplitudes. The implication is that where either EPR correlations or failure of local realism is predicted for continuous variable (quadrature phase amplitude) measurements, one can perform a modified experiment which would lead to conclusions about the much stronger premise of macroscopic local realism.
The violation of a Leggett–Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states—or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell’s locality premise. We follow recent work and propose the validity of a subset of Einstein–Podolsky–Rosen (EPR) and Leggett–Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett–Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the “element of reality” defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett–Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory.
Local realism reduces to the proposition that local determinate reality is the necessary and sufficient cause of every physical effect. By any standard account, quantum theory requires that local realism is false, because it embeds the famously spooky premise that some physical effects require causes that are instantly effective from arbitrarily far away. Nonetheless, quantum theory has replaced local realism as the foundation of science because, whereas local realism allegedly cannot violate the Bell inequality, quantum theory is taken to do so in accord with experiments. Here we prove, however, that an epistemic contextual model of local realism solves a puzzle about independent random measurements of local hidden variables in a way that causally explains observed Bell violations. We also reveal exactly how the Bell inequality fails to represent the local realistic prediction. Finally, we show that any theory that denies local realism comprises an unfalsifiable causal claim that is freely adjustable to make arbitrary predictions, which thus provide no validation of its causal claim. Results revitalize the hypothesis that local realism prevails. Keywords: Local Realism. Bell Violations. Photons. Entanglement. Quantum Physics.
In a Bell test, the set of observed probability distributions complying with the principle of local realism is fully characterized by Bell inequalities. Quantum theory allows for a violation of these inequalities, which is famously regarded as Bell nonlocality. However, finding the maximal degree of this violation is, in general, an undecidable problem. Consequently, no algorithm can be used to derive quantum analogs of Bell inequalities, which would characterize the set of probability distributions allowed by quantum theory. Here we present a family of inequalities, which approximate the set of quantum correlations in Bell scenarios where the number of settings or outcomes can be arbitrary. We derive these inequalities from the principle of Information Causality, and thus, we do not assume the formalism of quantum mechanics. Moreover, we identify a subspace in the correlation space for which the derived inequalities give the necessary and sufficient conditions for the principle of Macroscopic Locality. As a result, we show that in this subspace, the principle of Information Causality is strictly stronger than the principle of Macroscopic Locality.