arXiv subjects

Masanao Ozawa

Publications and source records attributed to Masanao Ozawa.

94 records · Page 6Linked to original sources

arXiv1997

The Problem of Measurement and the Theory of Quantum State Reduction

A new approach to the problem of measurement in quantum mechanics is proposed. In this approach, the process of measurement is described in the Heisenberg picture and divided into two stages. The first stage is to transduce the measured observable to the probe observable. The second stage is to amplify the probe observable to the macroscopic meter observable. Quantum state reduction is derived, based on the quantum Bayes principle, from the object-apparatus interaction in the first stage. The dynamical process of the second stage is described as a quantum amplification with infinite gain based on nonstandard analysis.

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arXiv1997

An Operational Approach to Quantum State Reduction

An operational approach to quantum state reduction, the state change of the measured system caused by a measurement of an observable conditional upon the outcome of measurement, is founded without assuming the projection postulate in any stages of the measuring process. Whereas the conventional formula assumes that the probe measurement satisfies the projection postulate, a new formula for determining the state reduction shows that the state reduction does not depend on how the probe observable is measured, or in particular does not depend on whether the probe measurement satisfies the projection postulate or not, contrary to the longstanding attempts in showing how the macroscopic nature of probe detection provokes state reduction.

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arXiv1997

Phase Operator Problem and Macroscopic Extension of Quantum Mechanics

To find the Hermitian phase operatorof a single-mode electromagnetic field in quantum mechanics, the Schroedinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is a Naimark extension of the optimal probability operator-valued measure for the phase parameter found by Helstrom. Eventually, the two promising approaches to the statistics of the phase in quantum mechanics is unified by means of the Hermitian phase operator in the macroscopic extension of the Schroedinger representation.

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arXiv1997

Quantum State Reduction and the Quantum Bayes Principle

This paper gives new foundations of quantum state reduction without appealing to the projection postulate for the probe measurement. For this purpose, the quantum Bayes principle is formulated as the most fundamental principle for determining the state of a quantum system, and the joint probability distribution for the outcomes of local successive measurements on a noninteracting entangled system is derived without assuming the projection postulate.

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