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New Journal of Physics

Nonlocality of the Schrödinger cat

Krzysztof Wódkiewicz

Published Sep 12, 2000• 30 citations
Publisher

Abstract

The nonlocality of the Schrödinger cat is established. A correlation measurement that exhibits quantum interference in the form of the Wigner function of the cat state is introduced. The relation of this correlation to quantum interference in phase space and the nonlocal character of the Schrödinger cat are discussed. It is shown that the Schrödinger cat correlation function leads to violation of the Bell inequality for macroscopically distinguishable states of the cat.

DOI
10.1088/1367-2630/2/1/321

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The nonlocality of the Schrödinger cat is established. A correlation measurement that exhibits quantum interference in the form of the Wigner function of the cat state is introduced. The relation of this correlation to quantum interference in phase space and the nonlocal character of the Schrödinger cat are discussed. It is shown that the Schrödinger cat correlation function leads to violation of the Bell inequality for macroscopically distinguishable states of the cat.
We propose an experimental scheme for testing nonlocality of a correlated two-mode quantum state of light. We show that the correlation functions violating the Bell inequalities in the proposed experiment are equal to the joint two-mode QQQ function and the Wigner function. This assigns a novel operational meaning to these two quasidistribution functions in tests of quantum nonlocality and also establishes a direct relationship between two intriguing aspects of quantum mechanics: the nonlocality of entangled states and the noncommutativity of quantum observables, which underlies the nonclassical structure of the phase-space quasidistribution functions.
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 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.