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13 - Entanglement, scaling, and the meaning of the wave function in protective measurement

from Part II - Meanings and implications

Published online by Cambridge University Press:  05 January 2015

By
Maximilian Schlosshauer  and
Tangereen V. B. Claringbold
Edited by
Shan Gao
Maximilian Schlosshauer
Affiliation:
University of Portland
Tangereen V. B. Claringbold
Affiliation:
University of Portland
Shan Gao
Affiliation:
Chinese Academy of Sciences
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Summary

We examine the entanglement and state disturbance arising in a protective measurement and argue that these inescapable effects doom the claim that protective measurement establishes the reality of the wave function. An additional challenge to this claim results from the exponential number of protective measurements required to reconstruct multi-qubit states. We suggest that the failure of protective measurement to settle the question of the meaning of the wave function is entirely expected, for protective measurement is but an application of the standard quantum formalism, and none of the hard foundational questions can ever be settled in this way.

Introduction

From the start, the technical result of protective measurement has been suggested to have implications for the interpretation of quantum mechanics. Consider how Aharonov and Vaidman [2] chose to begin their original paper introducing the idea of protective measurement:

We show that it is possible to measure the Schrödinger wave of a single quantum system. This provides a strong argument for associating physical reality with the quantum state of a single system.…

Since then, the pioneers of protective measurement seem to have taken a more moderate stance. Vaidman [42], in a recent synopsis of protective measurement, concedes that

the protective measurement procedure is not a proof that we should adopt one interpretation instead of the other, but it is a good testbed which shows advantages and disadvantages of various interpretations.

Notwithstanding this more subtle perspective and a number of critical studies of the technical and foundational aspects of protective measurement, Gao [21] has maintained, if not amplified, the force of Aharonov and Vaidman's original argument:

An immediate implication is that the result of a protective measurement, namely the expectation value of the measured observable in the measured state, reflects the actual physical property of the measured system, as the system is not disturbed after this result has been obtained.

[…]

Type
Chapter
Information
Protective Measurement and Quantum Reality
Towards a New Understanding of Quantum Mechanics
 , pp. 180 - 194
Publisher: Cambridge University Press
Print publication year: 2015

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