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arXiv:quant-ph/0101052

Proposal to test quantum mechanics against macroscopic realism using continuous variable entanglement: a definitive signature of a Schrödinger cat

M. D. Reid

Published Jan 12, 2001• 0 citations
arXivHTMLPDF

Abstract

In the Schrödinger-cat gedanken experiment a cat is in a quantum superposition of two macroscopically distinct states, alive and dead.The paradoxical interpretation of quantum mechanics is that the cat is not in one state or the other, alive or dead, immediately prior to its measurement. Because of this apparent defiance of macroscopic reality, quantum superpositions of states macroscopically distinct have generated much interest. Here we address the issue of proving a contradiction with macroscopic reality objectively, through the testable predictions of quantum mechanics. We consider the premises of macroscopic reality (that the ``cat'' is either ``dead'' or ``alive'', the measurement indicating which) and macroscopic locality (that simultaneous measurements some distance away cannot induce the macroscopic change, ``dead'' to ``alive'' and vice versa, to the ``cat''). The predictions of quantum mechanics for certain states, generated using states exhibiting continuous variable entanglement, are shown to be incompatible with the predictions of all theories based on this dual premise. Our proof is along the lines of Bell's theorem, but where all relevant measurements give macroscopically distinct results.

DOI
10.48550/arxiv.quant-ph/0101052

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In the Schrödinger-cat gedanken experiment a cat is in a quantum superposition of two macroscopically distinct states, alive and dead.The paradoxical interpretation of quantum mechanics is that the cat is not in one state or the other, alive or dead, immediately prior to its measurement. Because of this apparent defiance of macroscopic reality, quantum superpositions of states macroscopically distinct have generated much interest. Here we address the issue of proving a contradiction with macroscopic reality objectively, through the testable predictions of quantum mechanics. We consider the premises of macroscopic reality (that the cat'' is either dead'' or alive'', the measurement indicating which) and macroscopic locality (that simultaneous measurements some distance away cannot induce the macroscopic change, dead'' to alive'' and vice versa, to the cat''). The predictions of quantum mechanics for certain states, generated using states exhibiting continuous variable entanglement, are shown to be incompatible with the predictions of all theories based on this dual premise. Our proof is along the lines of Bell's theorem, but where all relevant measurements give macroscopically distinct results.
Abstract In the Schrödinger cat gedanken experiment a “cat” is in a quantum superposition of two macroscopically distinct states. There is the apparent interpretation that the “cat” is not in one state or the other, “alive” or “dead”. Here this interpretation is proved objectively. I propose the following definition of macroscopic reality: first, that the “cat” is either dead or alive, the measurement revealing which; second, that measurements on other “cats” some distance away cannot induce the macroscopic change, “dead” to “alive” and vice versa, to the “cat”. The predictions of quantum mechanics are shown to be incompatible with this premise.
This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as ‘Schrodinger’s cat’, has long posed an apparent paradox because the state resulting from a measurement appears to be a quantum superposition in which the detector is in two macroscopically distinct states (alive and dead in the case of the cat) simultaneously. Many alternative interpretations of the quantum mathematical formalism, and several alternative modifications of the theory, have been proposed to resolve this problem, but no consensus has formed supporting any one of them. Applying standard quantum theory to the measurement state, together with the analysis and results of decades of nonlocality experiments with pairs of entangled systems, this paper shows the entangled measurement state is not a paradoxical macroscopic superposition of states. It is instead a phase-dependent superposition of correlations between states of the subsystems. Thus Schrodinger’s cat is a non-paradoxical ‘macroscopic correlation’ in which one of the two correlated systems happens to be a detector. This insight resolves the problem of definite outcomes but it does not entirely resolve the measurement problem because the entangled state is still reversible.
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub-systems. This is not paradoxical. Standard quantum theory rigorously predicts the experimentally-observed outcomes of this state. Neither sub-system is superposed; rather, the correlations between the states of the subsystems are superposed. This resolves the problem of definite outcomes. The nonlocal properties of entanglement then ensure that only one outcome occurs while the other outcome simultaneously does not occur, resolving a problem posed by Einstein in 1927. The single outcome that occurs then triggers an irreversible process leading to macroscopic registration of the outcome. This resolves the quantum measurement problem. Collapse occurs because of entanglement and does not require a special collapse postulate. Collapse is a consequence of standard quantum physics and the irreversible nature of the macroscopic registration.
The Schrodinger's Cat paradox was proposed in 1935 by Edwin Schrodinger, one of the founders of quantum mechanics, as an attempt to visualize the macroscopic realization of a quantum superposition state. A cat is placed in a sealed box together with a vial of poison. A two-state particle (e.g. an electron) is sent into a detector in the box resulting either in a broken or an intact vial and a dead or live cat, respectively. The main problem consists in whether the superposition state of a microscopic particle can be transferred upon the macroscopic cat, that is, whether the cat can exist in a superposition state, being simultaneously dead and alive. Since the standard Copenhagen interpretation is unable to assign any reality to the quantum superposition state, the paradox finds no resolution within the regime of this interpretation. Von Neumann's insistence on the uniform treatment of both microscopic (quantum) and macroscopic (classical) objects according to the laws of quantum mechanics provides a more consistent framework for the resolution of the paradox. In particular, the discovery of the phenomenon of decoherence, whereby the disappearance of the quantum interferences at the macro level is accounted for, suggests the onset of an extremely efficient interference relaxation process (10-23 s) upon the interaction of the two state particle with the detector. As a result, Schrodinger's cat can exist macroscopically either as dead or alive and never as a combination of both. Decoherence not only aids the resolution of the Schrodinger's Cat paradox but also sheds light upon the mechanisms by which the macro-world emerges from the microscopic quantum realm.
The entangled state that results when a detector measures a superposed quantum system has spawned decades of concern about the problem of definite outcomes or "Schrodinger's cat." This state seems to describe a detector in an indefinite or "smeared" situation of indicating two macroscopic configurations simultaneously. This would be paradoxical. Since all entangled states are known to have nonlocal properties, and since measurements have obvious nonlocal characteristics, it's natural to turn to nonlocality experiments for insight into this question. Unlike the measurement situation where the phase is fixed at zero for perfect correlations, nonlocality experiments cover the full range of superposition phases and can thus show precisely what entangled states superpose. For two-state systems, these experiments reveal that the measurement state is not a superposition of two macroscopically different detector states but instead a superposition of two coherent correlations between distinct detector states and corresponding system states. In the measurement situation (i.e. at zero phase), and assuming the Schrodinger's cat scenario, the entangled state can be read as follows: An undecayed nucleus is perfectly correlated with an alive cat, AND a decayed nucleus is perfectly correlated with a dead cat, where "AND" indicates the superposition. This is not paradoxical.
Schrödinger's famous Gedankenexperiment has inspired multiple generations of physicists to think about apparent paradoxes that arise when the logic of quantum physics is applied to macroscopic objects. The development of quantum technologies enabled us to produce physical analogues of Schrödinger's cats, such as superpositions of macroscopically distinct states as well as entangled states of microscopic and macroscopic entities. Here we take one step further and prepare an optical state which, in Schrödinger's language, is equivalent to a superposition of two cats, one of which is dead and the other alive, but it is not known in which state each individual cat is. Specifically, the alive and dead states are, respectively, the displaced single photon and displaced vacuum (coherent state), with the magnitude of displacement being on a scale of 10810^8108 photons. These two states have significantly different photon statistics and are therefore macroscopically distinguishable.