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Physical Review A

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

Orly Alter, Y. Yamamoto

Published May 1, 1996• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.53.r2911

Related papers

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 A•Jul 1, 1997•11 citations

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].

Cambridge University Press eBooks•Nov 30, 2014•9 citations

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

Yakir Aharonov, Lev Vaidman A

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.

arXiv:quant-ph/9612045•Physical Review A•Jul 1, 1997•7 citations

How to protect the interpretation of the wave function against protective measurements

Jos Uffink

A new type of procedures, called protective measurements, was proposed by Aharonov, Anandan, and Vaidman [Phys. Rev. A 97, 4616 (1993); Found. Phys. 26, 117 (1996)]. These authors argued that a protective measurement allows the determination of arbitrary observables of a single quantum system, and claimed that this favors a realistic interpretation of the quantum state. This paper proves that only observables that commute with the system's Hamiltonian can be measured protectively. It is argued that this restriction saves the coherence of alternative interpretations.

arXiv:quant-ph/9903007•Physical Review A•Nov 1, 1999•59 citations

Critique of protective measurements

N. D. Hari Dass, Tabish Qureshi

The recently proposed idea of ``protective'' measurement of a quantum state is critically examined, and generalized. Earlier criticisms of the idea are discussed, and their relevance to the proposal assessed. Several constraints on measuring apparatus required by ``protective'' measurements are discussed, with emphasis on how they may restrict their experimental feasibility. Though ``protective'' measurements result in an unchanged system state and a shift of the pointer proportional to the expectation value of the measured observable in the system state, the actual reading of the pointer position gives rise to several subtleties. We propose several schemes for reading the pointer position, both when the apparatus is treated as a classical system as well as when its quantum aspects are taken into account, that address these issues. The tiny entanglement which is always present due to deviation from extreme adiabaticity in realistic situations is argued to be the weakest aspect of the proposal. Because of this, one can never perform a protective measurement on a single quantum system with absolute certainty. This clearly precludes an ontological status for the wave function. Several other conceptual issues are also discussed.

arXiv:quant-ph/9805012•Physical Review A•Apr 1, 1999•48 citations

Meaning of the wave function

Yakir Aharonov, J. Anandan, Lev Vaidman A

So far, the wave function has been interpreted as a probability amplitude, which is given physical meaning by ensemble averages of a large number of identical systems at a given time. We give an alternative interpretation of the wave function for a single system by means of a measurement which lasts a long time. This is a measurement on a single quantum system which determines the expectation values of (not necessarily commuting) observables while the wave function is protected from collapsing because it undergoes another suitably chosen interaction. This type of measurement enables the distinction between states which are not orthogonal, but are protected by a suitable interaction with the states of their environment, even for a single system. It therefore gives a different ontological meaning to the wave function. Several experiments in which such a measurement is realized, which can in principle be performed using electrons, neutrons, or atoms, are studied.

Physical Review A•Jun 1, 1993•300 citations
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.
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.
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].
A new type of procedures, called protective measurements, was proposed by Aharonov, Anandan, and Vaidman [Phys. Rev. A 97, 4616 (1993); Found. Phys. 26, 117 (1996)]. These authors argued that a protective measurement allows the determination of arbitrary observables of a single quantum system, and claimed that this favors a realistic interpretation of the quantum state. This paper proves that only observables that commute with the system's Hamiltonian can be measured protectively. It is argued that this restriction saves the coherence of alternative interpretations.
The recently proposed idea of ``protective'' measurement of a quantum state is critically examined, and generalized. Earlier criticisms of the idea are discussed, and their relevance to the proposal assessed. Several constraints on measuring apparatus required by ``protective'' measurements are discussed, with emphasis on how they may restrict their experimental feasibility. Though ``protective'' measurements result in an unchanged system state and a shift of the pointer proportional to the expectation value of the measured observable in the system state, the actual reading of the pointer position gives rise to several subtleties. We propose several schemes for reading the pointer position, both when the apparatus is treated as a classical system as well as when its quantum aspects are taken into account, that address these issues. The tiny entanglement which is always present due to deviation from extreme adiabaticity in realistic situations is argued to be the weakest aspect of the proposal. Because of this, one can never perform a protective measurement on a single quantum system with absolute certainty. This clearly precludes an ontological status for the wave function. Several other conceptual issues are also discussed.
So far, the wave function has been interpreted as a probability amplitude, which is given physical meaning by ensemble averages of a large number of identical systems at a given time. We give an alternative interpretation of the wave function for a single system by means of a measurement which lasts a long time. This is a measurement on a single quantum system which determines the expectation values of (not necessarily commuting) observables while the wave function is protected from collapsing because it undergoes another suitably chosen interaction. This type of measurement enables the distinction between states which are not orthogonal, but are protected by a suitable interaction with the states of their environment, even for a single system. It therefore gives a different ontological meaning to the wave function. Several experiments in which such a measurement is realized, which can in principle be performed using electrons, neutrons, or atoms, are studied.