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Ensemble interpretations of quantum mechanics. A modern perspective

Abstract A discussion of aspects of probability relevant to the differing interpretations of quantum theory is given, followed by an account of so-called orthodox interpretations of quantum theory that stresses their flexibility and subtlety as well as their problems. An account of ensemble interpretations is then presented, with discussion of the approaches of Einstein and Ballentine, and of later developments, including those interpretations usually called “stochastic”. A general study of ensemble interpretations follows, including investigation of PIV (premeasurement initial values) and minimal interpretations, an account of recent developments, and an introduction to unsharp measurements. Finally, application is made to particular problems, EPR, Schrodingers cat, the quantum Zeno “paradox”, and Bells theorem.

Generic Entanglement Generation, Quantum Statistics, and Complementarity

A general and an arbitrarily efficient scheme for entangling the spins (or any spinlike degree of freedom) of two independent uncorrelated identical particles by a combination of two particle interferometry and which way detection is formulated. It is shown that the same setup could be used to identify the quantum statistics of the incident particles from either the sign or the magnitude of measured spin correlations. Our setup also exhibits a curious complementarity between particle distinguishability and the amount of generated entanglement.

An experiment to throw more light on light

Abstract We propose an experiment in which “single photon states” are incident on a combination of two prisms placed opposite each other. When the gap between the prisms is larger than the wavelength, the incident “photon states” suffer total internal reflection inside the first prism (registered by counter 1). When the gap is shorter than the wavelength, there is a possibility of their tunneling across the gap (registered by counter 2). The two counters 1 and 2 clicking in perfect anticoincidence would show simultaneously sharp particle and wave characteristics, highlighting inadequacy of the complementarity principle in its usual form. Other possibilities of the outcome are not favoured by the formalism of quantum optics.

Bell's inequality for a single spin-1/2 particle and quantum contextuality

Abstract We argue that for a single particle Bells inequality is a consequence of noncontextuality and is incompatible with statistical predictions of quantum mechanics. Thus noncontextual models can be empirically falsified, independent of locality condition. For this an appropriate entanglement between disjoint Hilbert spaces pertaining to translational and spin degrees of freedom of a single spin-1/2 particle is invoked.

A curious gedanken example of the Einstein-Podolsky-Rosen paradox using CP nonconservation

Abstract We consider the effect of CP noninvariance in the Einstein-Podolsky-Rosen (EPR) type gedanken example involving neutral pseudo-scalar mesons originating from the decay of a JPC = 1−− vector meson. In principle at least, this leads to the intriguing possibility of incompatibility between quantum mechanics (incorporating CP violation) and Einsteins locality condition at the statistical level.

Reflections on the quantum Zeno paradox

The authors clarify some of the controversial aspects involved in the treatment of the quantum Zeno paradox. An argument for the paradox is given on the basis of the uncertainty principle, and the conditions for the paradox are analysed. Flemings rule is proved in a simple way. Connection with the standard time-dependent perturbation theory is discussed. They compare the Zeno paradox with the other well known paradoxes of quantum mechanics and point out that the quantum Zeno paradox is immune to the use of the ensemble interpretation which has some success in tackling the other paradoxes. Remarks are made concerning the broader significance of the quantum Zeno paradox.

A critical re-examination of the quantum Zeno paradox

The quantum Zeno paradox is defined as a negative-result experiment involving a macroscopic apparatus, and distinguished from other quantum Zeno processes. It is demonstrated that collapse of state-vector is not a requirement for the paradox, which is independent of interpretation of quantum theory. Gedanken experiments are outlined which illustrate the key features of the paradox, and its implications for the realist interpretation are discussed.

A unified framework for quantum Zeno processes

Abstract The genesis of quantum Zeno type results is shown to be in the suppression of “regeneration” terms in the state-vector. In the absence of intermediate effects, the “decayed” component of the state-vector at one time gives rise to a “surviving” component at later times. Intermediate effects can suppress this effect; they may be observations as in the original quantum Zeno “paradox”, or microscopic interactions. Thus all such processes are shown to be analogous formally, though of different status conceptually.

An «experiment to throw more light on light» : implications

Abstract Mizobuchi and Ohtake [Phys. Lett. A 168 (1992) 1] have performed the double-prism experiment with single photon states proposed by us [Phys. Lett. A 153 (1991) 403] and verified the quantum optical prediction outlined in that paper. Here we give a detailed justification of our claim that this experimental result contradicts the tenet of mutual exclusiveness of classical wave and particle pictures assumed in Bohrs complementarity principle.

Is quantum mechanics with CP nonconservation incompatible with Einstein's locality condition at the statistical level?

As a sequel to our earlier work, we present a general analysis, in terms of density operators, of the EPR-type gedanken situation (in the presence of CP noninvariance) involving basis states which are mutually non-orthogonal but partially distinguishable. We also comment on the published criticisms of our earlier work.