A quantum-mechanical theory of distant correlations

Abstract

A composite quantum system consisting of two distant subsystems and described by a correlated state vector φ12 is considered. It was shown in a previous work by the authors [Ann. Phys. 96, 382 (1976)] that such a system can be equivalently described in terms of the reduced statistical operators ρ1 and ρ2 of φ12 applying to the subsystems and a correlation operator Ua between them. It is argued that this description has a firm physical foundation for the system considered in view of the fact that, on account of the subsystems being distant, one can only measure pairs of subsystem observables A1, B2 in coincidence. The direct measurement of A1 such that [A1,ρ1]=0 on the ensemble of first subsystems performs distantly (without interaction) an orthogonal decomposition of the ensemble of second subsystems ρ2, that amounts to the measurement of the twin observable A2 (A2≡UaA1U−1aQ2, Q2 being the range projector of ρ2). A number of coincidence experiments have confirmed this claim, and have disproved all attempts (on the quantum and on the subquantum levels) to view this decomposition of ρ2 as being present also before the measurement of A1. Hence, this decomposition into subensembles comes about in the very measurement of A1, and Ua determines them in a simple way. It is demonstrated that Ua is essential for twin observables and twin symmetry operators. A detailed study of these operators is presented from a unified point of view. Puzzling features of quantum correlations described by Ua show up in composite states when the mentioned distant decompositions of ρ2 into subensembles can be incompatible with one another. A general definition of such φEPR12 states (called Einstein–Podolsky–Rosen states) is given in a few equivalent forms, and the nonuniqueness of the Schmidt canonical form of φEPR12 is investigated in order to encourage further theoretical and experimental exploration of distant quantum correlations.