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Distinct Quantum States Cannot Be Compatible with a Single State of Reality

Shan Gao

Published Mar 8, 2013• 1 citation
OpenAlex

Abstract

It is demonstrated that, based on an analysis of protective measurements, distinct quantum states cannot be compatible with a single state of reality. Recently Lewis et al (2012) demonstrated that additional assumptions such as preparation independence are always necessary to rule out a ψ-epistemic model, in which the quantum state is not uniquely determined by the under-lying physical state. Their conclusion is based on an analysis of conventional projective measurements. Here we will demonstrate that protective measure-ments (Aharonov and Vaidman 1993; Aharonov, Anandan and Vaidman 1993), which are distinct from projective measurements, already shows that distinct quantum states cannot be compatible with a single state of reality. Projective measurements are one kind of measurements, for which the cou-pling between the measuring device and the measured system is very strong and almost instantaneous, and the measurement results are the eigenvalues of the measured observable. Due to the resulting collapse of the wave function, such impulsive measurements cannot measure the actual physical state of the measured system (when the system is not in one of the eigenstates of the mea-sured observable). This seems to leave space for ψ-epistemic models (Lewis et al 2012). However, it has been known that the coupling strength and the measuring time can be adjusted for a standard measurement procedure, and there also exist other kinds of measurements such as weak measurements and

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Comment on "Distinct Quantum States Can Be Compatible with a Single State of Reality"

Shan Gao

In their Letter [1], Lewis et al. demonstrated that additional assumptions such as preparation independence are always necessary to rule out a ψ-epistemic model, in which the quantum state is not uniquely determined by the underlying physical state. Here we point out that these authors ignored the important work of Aharonov, Anandan and Vaidman on protective measurements [2-5], and their conclusion, which is based only on an analysis of conventional projective measurements, is not true. Projective measurements are one kind of measurements, for which the cou-pling between the measuring device and the measured system is very strong and almost instantaneous, and the measurement results are the eigenvalues of the measured observable. Due to the resulting collapse of the wave function, such impulsive measurements cannot measure the actual physical state of the measured system. This seems to leave space for ψ-epistemic models [1]. Thanks to the work of Aharonov et al, however, it has been known that the coupling strength and the measuring time can be adjusted for a standard measurement

•Nov 23, 2012•0 citations

Notes on the reality of the quantum state

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Based on an analysis of protective measurements, we show that the quantum state represents the physical state of a single quantum system. This result is more definite than the PBR theorem [Pusey, Barrett, and Rudolph, Nature Phys. 8, 475 (2012)]. The physical meaning of the quantum state is an important interpreta-tive problem of quantum mechanics. A long-standing question is whether a pure state relates only to an ensemble of identically prepared systems or di-rectly to the state of a single system. Recently, Pusey, Barrett and Rudolph (PBR) demonstrated that under an independence assumption, the quantum state is a representation of the physical state of a single quantum system [1]. This poses a further interesting question, namely whether ψ-ontology can be argued without resorting to nontrivial assumptions such as the in-dependence assumption (cf. Ref. [2-4]). In this Letter, we will show that protective measurements [5,6] already provide such an argument. The meaning of the quantum state is usually analyzed in the context of conventional impulsive measurements of an ensemble of identically prepared systems. However, it has been known that the quantum state of a single prepared system can be protectively measured [5-9]. During a protective measurement, the measured system is protected by an appropriate procedure (e.g. via the quantum Zeno effect) so that its quantum state neither changes nor becomes entangled with the quantum state of the measuring device appreciably. In this way, such protective measurements can measure the expectation values of observables from a single quantum system, even if the system is initially not in an eigenstate of the measured observable, and in particular, the quantum state of the system can also be measured as expectation values of certain observables. It is expected that protective measurements will be realized in the near future with the rapid development of quantum technologies.

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Reality of the quantum state: A new proof in terms of protective measurements

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The ontological model framework provides a rigorous approach to address the question of whether the quantum state is ontic or epistemic. When considering only conventional projective measurements, auxiliary assumptions are always needed to prove the reality of the quantum state in the framework. For example, the Pusey-Barrett-Rudolph theorem is based on an additional preparation independence assumption. In this paper, we give a new proof of psi-ontology in terms of protective measurements in the ontological model framework. It is argued that the proof needs not rely on auxiliary assumptions, and also applies to deterministic theories such as the de Broglie-Bohm theory. In addition, we give a simpler argument for psi-ontology beyond the framework, which is only based on protective measurements and a weaker criterion of reality. The argument may be also appealing for those people who favor an anti-realist view of quantum mechanics.

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

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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.

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A PBR-like argument for psi-ontology in terms of protective measurements

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The ontological status of the wave function in quantum mechanics has been analyzed in the context of conventional projective measurements. These analyses are usually based on some nontrivial assumptions, e.g. a preparation independence assumption is needed to prove the PBR theorem. In this paper, we give a PBR-like argument for psi-ontology in terms of protective measurements, by which one can directly measure the expectation values of observables on a single quantum system. The proof does not resort to nontrivial assumptions such as preparation independence assumption.

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Distinct Quantum States Can Be Compatible with a Single State of Reality

Peter G. Lewis, David H. Jennings, Jonathan Barrett +1 more

Perhaps the quantum state represents information about reality, and not reality directly. Wave function collapse is then possibly no more mysterious than a Bayesian update of a probability distribution given new data. We consider models for quantum systems with measurement outcomes determined by an underlying physical state of the system but where several quantum states are consistent with a single underlying state-i.e., probability distributions for distinct quantum states overlap. Significantly, we demonstrate by example that additional assumptions are always necessary to rule out such a model.

arXiv:1201.6554•Physical Review Letters•Oct 9, 2012•149 citations
It is demonstrated that, based on an analysis of protective measurements, distinct quantum states cannot be compatible with a single state of reality. Recently Lewis et al (2012) demonstrated that additional assumptions such as preparation independence are always necessary to rule out a ψ-epistemic model, in which the quantum state is not uniquely determined by the under-lying physical state. Their conclusion is based on an analysis of conventional projective measurements. Here we will demonstrate that protective measure-ments (Aharonov and Vaidman 1993; Aharonov, Anandan and Vaidman 1993), which are distinct from projective measurements, already shows that distinct quantum states cannot be compatible with a single state of reality. Projective measurements are one kind of measurements, for which the cou-pling between the measuring device and the measured system is very strong and almost instantaneous, and the measurement results are the eigenvalues of the measured observable. Due to the resulting collapse of the wave function, such impulsive measurements cannot measure the actual physical state of the measured system (when the system is not in one of the eigenstates of the mea-sured observable). This seems to leave space for ψ-epistemic models (Lewis et al 2012). However, it has been known that the coupling strength and the measuring time can be adjusted for a standard measurement procedure, and there also exist other kinds of measurements such as weak measurements and
In their Letter [1], Lewis et al. demonstrated that additional assumptions such as preparation independence are always necessary to rule out a ψ-epistemic model, in which the quantum state is not uniquely determined by the underlying physical state. Here we point out that these authors ignored the important work of Aharonov, Anandan and Vaidman on protective measurements [2-5], and their conclusion, which is based only on an analysis of conventional projective measurements, is not true. Projective measurements are one kind of measurements, for which the cou-pling between the measuring device and the measured system is very strong and almost instantaneous, and the measurement results are the eigenvalues of the measured observable. Due to the resulting collapse of the wave function, such impulsive measurements cannot measure the actual physical state of the measured system. This seems to leave space for ψ-epistemic models [1]. Thanks to the work of Aharonov et al, however, it has been known that the coupling strength and the measuring time can be adjusted for a standard measurement
Based on an analysis of protective measurements, we show that the quantum state represents the physical state of a single quantum system. This result is more definite than the PBR theorem [Pusey, Barrett, and Rudolph, Nature Phys. 8, 475 (2012)]. The physical meaning of the quantum state is an important interpreta-tive problem of quantum mechanics. A long-standing question is whether a pure state relates only to an ensemble of identically prepared systems or di-rectly to the state of a single system. Recently, Pusey, Barrett and Rudolph (PBR) demonstrated that under an independence assumption, the quantum state is a representation of the physical state of a single quantum system [1]. This poses a further interesting question, namely whether ψ-ontology can be argued without resorting to nontrivial assumptions such as the in-dependence assumption (cf. Ref. [2-4]). In this Letter, we will show that protective measurements [5,6] already provide such an argument. The meaning of the quantum state is usually analyzed in the context of conventional impulsive measurements of an ensemble of identically prepared systems. However, it has been known that the quantum state of a single prepared system can be protectively measured [5-9]. During a protective measurement, the measured system is protected by an appropriate procedure (e.g. via the quantum Zeno effect) so that its quantum state neither changes nor becomes entangled with the quantum state of the measuring device appreciably. In this way, such protective measurements can measure the expectation values of observables from a single quantum system, even if the system is initially not in an eigenstate of the measured observable, and in particular, the quantum state of the system can also be measured as expectation values of certain observables. It is expected that protective measurements will be realized in the near future with the rapid development of quantum technologies.
The ontological model framework provides a rigorous approach to address the question of whether the quantum state is ontic or epistemic. When considering only conventional projective measurements, auxiliary assumptions are always needed to prove the reality of the quantum state in the framework. For example, the Pusey-Barrett-Rudolph theorem is based on an additional preparation independence assumption. In this paper, we give a new proof of psi-ontology in terms of protective measurements in the ontological model framework. It is argued that the proof needs not rely on auxiliary assumptions, and also applies to deterministic theories such as the de Broglie-Bohm theory. In addition, we give a simpler argument for psi-ontology beyond the framework, which is only based on protective measurements and a weaker criterion of reality. The argument may be also appealing for those people who favor an anti-realist view of quantum mechanics.
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 ontological status of the wave function in quantum mechanics has been analyzed in the context of conventional projective measurements. These analyses are usually based on some nontrivial assumptions, e.g. a preparation independence assumption is needed to prove the PBR theorem. In this paper, we give a PBR-like argument for psi-ontology in terms of protective measurements, by which one can directly measure the expectation values of observables on a single quantum system. The proof does not resort to nontrivial assumptions such as preparation independence assumption.
Perhaps the quantum state represents information about reality, and not reality directly. Wave function collapse is then possibly no more mysterious than a Bayesian update of a probability distribution given new data. We consider models for quantum systems with measurement outcomes determined by an underlying physical state of the system but where several quantum states are consistent with a single underlying state-i.e., probability distributions for distinct quantum states overlap. Significantly, we demonstrate by example that additional assumptions are always necessary to rule out such a model.