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International Journal of Quantum Information

DESTRUCTION OF QUANTUM STATES OVER DISCRETE AND CONTINUOUS VARIABLES

Paweł Caban, Jakub Rembieliński, Kordian A. Smoliński, Zbigniew Walczak

Published Dec 1, 2004• 0 citations
Publisher

Abstract

Prediction of the correlation between the data does not cause any problems in an ideal Einstein–Podolsky–Rosen (EPR) experiment, but if both measurements are not really performed at the same time one should take into account that a particle is irreversibly absorbed by a detector during the measurement. We calculate with full details the destruction of quantum states during the spin measurement of a particle involving localization of a particle in a detector in a system of two distinguishable particles of spin-½ and consider an example of the destruction in the configuration typical for EPR experiments.

DOI
10.1142/s0219749904000468

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Prediction of the correlation between the data does not cause any problems in an ideal Einstein–Podolsky–Rosen (EPR) experiment, but if both measurements are not really performed at the same time one should take into account that a particle is irreversibly absorbed by a detector during the measurement. We calculate with full details the destruction of quantum states during the spin measurement of a particle involving localization of a particle in a detector in a system of two distinguishable particles of spin-½ and consider an example of the destruction in the configuration typical for EPR experiments.
In this paper we calculate with full details Einstein-Podolsky-Rosen spin correlations in the framework of nonrelativistic quantum mechanics. We consider the following situation: two-particle state is prepared (we consider separately distinguishable and identical particles and take into account the space part of the wave function) and two observers in relative motion measure the spin component of the particle along given directions. The measurements are performed in bounded regions of space (detectors), not necessarily simultaneously. The resulting correlation function depends not only on the directions of spin measurements but also on the relative velocity of the observers.
Quantum mechanics allows for multiple predictions for the outcome of an EPR experiment. The correct calculation must be used, guided by the physical conditions of the experiment. The quantum joint prediction for EPR correlation is derived and shown to involve a single sampling. The solution for separated measurement, where there are two private samplings, is then developed using orthodox quantum mechanics with Luders' rule for state projection on measurement. The separated solution is shown to duplicate the predictions of the quantum joint solution. However, it is shown that this solution requires superluminal transmission of information and therefore it is physically impossible. Alternative predictions respecting special relativity are developed using both Von Neumann projection and null projection (no projection at all). Conditions for the proper application of state projection rules are considered and Luders' rule is identified as the primary culprit in the EPR paradox. It cannot be applied to EPR.
The question of how to deal with inefficient detectors in actual experiments of the Einstein-Podolsky-Rosen type is studied. We derive the necessary and sufficient condition for compatibility with local realism of data collected in experiments with two settings of each detector, without making auxiliary assumptions about undetected events. For the conventional experiment with particles in the singlet state (or its photon analogue), the data predicted by the quantum theory do not violate this condition unless the quantum efficiency of the detectors exceeds 83%.
We first consider the Einstein-Podolsky-Rosen (EPR) paradox for the system of two particles with spin 1/2 with entangled spins in first-quantized quantum mechanics (QM). If measurement is governed by wavefunction collapse, then gedanken experiments show that a number of fundamental principles including conservation of angular momentum and the Heisenberg uncertainty principle can be violated. We conclude that the collapse of the spin part of the wavefunction cannot happen and therefore an EPR paradox does not arise for this system. QM unitarity alone is sufficient to rule out "spooky" action at a distance. The absence of spin wavefunction collapse leads to several interesting conclusions about how measurement works in QM: When wavefunction collapse does not happen, (i) a signal from a macroscopic measuring device indicating that a system is in a state S does not necessarily mean that it is or was in S and (ii) the uncertainty in QM at the microscopic level is transmitted to uncertainty in signals for the macroscopic measuring device. We derive two general results on how quantum measurement works and illustrate them in a spin-1/2 measurement. In contrast to first-quantized QM, in quantum field theory we are unable to fully rule out the possibility of wavefunction collapse. However, when we insist on unitarity (thereby excluding the possibility of wavefunction collapse) and additionally take into account in the wavefunction all degrees of freedom involved in the measurement (including those of the equipment, experimentalists, etc.), a consistant acceptable understanding of the Bell-inequality-type experiments involving entangled photon polarizations emerges including the absence of an EPR paradox. The ability of an experimentalist to be aware of his perceptions but unable to be conscious of other components of a generalized Schrodinger Cat plays a role in resolving the Measurement Problem.