arXiv:quant-ph/9612045 · Physical Review A

Comment on “Protective measurement of the wave function of a single squeezed harmonic-oscillator state”

Yakir Aharonov, Lev Vaidman A

Published Jul 1, 1997• 7 citations

Abstract

Alter and Yamamoto [Phys. Rev. A 53, R2911 (1996)] claimed to consider ``protective measurements'' that we have recently introduced. We show that the measurements discussed by Alter and Yamamoto are not the protective measurements we proposed. Therefore, their results are irrelevant to the nature of protective measurements.

DOI: 10.1103/physreva.56.1055

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Reply to “Comment on ‘Protective measurement of the wave function of a single squeezed harmonic-oscillator state”’

Orly Alter, Y. Yamamoto

The adiabatic ``protective measurement'' suggested by Aharonov, Anandan, and Vaidman [Phys. Lett. A 178, 38 (1993)] is a measurement of a discrete energy eigenstate, in which the entanglement between the measured state and the quantum probe is avoided approximately when they interact adiabatically, and the measured state is left approximately unchanged (up to a phase factor) for all measured observables. This measurement scheme, however, does not overcome the reduction of the measured state, because this state is only approximately, and not exactly, disentangled from the quantum probe. Our recent analysis of a measurement scheme of a squeezed harmonic-oscilllator state [Phys. Rev. A 53, R2911 (1996)], in which the entanglement between the measured state and the probe is avoided exactly, and the measured state is left exactly unchanged (up to a phase factor) for all measured observables, suggests that in order to measure the quantum state of a single system without changing this state, full a priori information about this state is required.

Physical Review AJul 1, 199711 citations

Protective measurement of the wave function of a single squeezed harmonic-oscillator state

Orly Alter, Y. Yamamoto

A scheme for the "protective measurement" [Phys. Rev. A 47, 4616 (1993)] of the wave function of a squeezed harmonic-oscillator state is described. This protective measurement is shown to be equivalent to a measurement of an ensemble of states. The protective measurement, therefore, allows for a definition of the quantum wave function on a single system. Yet, this equivalency also suggests that both measurement schemes account for the epistemological meaning of the wave function only. The protective measurement requires a full a priori knowledge of the measured state. The intermediate cases, in which only partial a priori information is given, are also discussed.

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Protective measurement of the wave function of a single system

Lev Vaidman A

My view on the meaning of the quantum wave function and its connection to protective measurements is described. The wave function and only the wave function is the ontology of the quantum theory. Protective measurements support this view although they do not provide a decisive proof. A brief review of the discovery and the criticism of protective measurement is presented. Protective measurements with postselection are discussed. Introduction In the first graduate course of quantum mechanics I remember asking the question: “Can we consider the wave function as a description of a single quantum system?” I got no answer. Twelve years later, in South Carolina, after I completed my Ph.D. studies at Tel Aviv University under the supervision of Yakir Aharonov in which we developed the theory of weak measurements [1], I asked Aharonov: Can we use weak measurement to observe the wave function of a single particle? At that time I had already become a strong believer in the many-worlds interpretation (MWI) of quantum mechanics [2] and had no doubt that a single system is described by the wave function. Yakir Aharonov never shared with me the belief in the MWI. When we realized that using what is called now protective measurement , we can, under certain conditions, observe the wave function of a single quantum system, he was really excited by the result. At 1992 I was invited to a conference on the Foundations of Quantum Mechanics in Japan where I presented this result: “The Schrödinger wave is observable after all!”[3]. Then I went home to Tel Aviv where I finished writing a letter which received mixed reviews in Phys. Rev. Lett. , while Jeeva Anandan, working on the topic with Aharonov in South Carolina, wrote a paper accepted in Phys. Rev. A [4]. After acceptance of the PRA paper it was hard to fight the referees in PRL, but PLA accepted it immediately [5].

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Quantum Measurement of a Single System

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