Why protective measurement does not establish the reality of the quantum state

Joshua Combes; Christopher Ferrie; Matthew S. Leifer; Matthew Fairbairn Pusey

doi:10.1007/s40509-017-0111-4

Why protective measurement does not establish the reality of the quantum state

Joshua Combes, Christopher Ferrie, Matthew S. Leifer, Matthew Fairbairn Pusey

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

“Protective measurement” refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a “protecting” operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconstruct the quantum state in a different way via process tomography. Our second argument is based on exact analyses of special cases of protective measurement, and our final argument is to construct explicit “휓-epistemic” toy models for protective measurement, which strongly suggest that protective measurement does not imply the reality of the quantum state. The common theme of the three arguments is that almost all of the information comes from the “protection” operation rather than the quantum state of the system, and hence the schemes have no implications for the reality of the quantum state.

Original language	English
Pages (from-to)	189-211
Number of pages	23
Journal	Quantum Studies: Mathematics and Foundations
Volume	5
DOIs	https://doi.org/10.1007/s40509-017-0111-4
Publication status	Published - 14 Jul 2017

Bibliographical note

This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

Access to Document

10.1007/s40509-017-0111-4

Why protective measurement does not establish the reality of the quantum state
This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details
Accepted author manuscript, 527 KB

https://arxiv.org/abs/1509.08893

Cite this

@article{ce1090ed2a104119a3cb84d08aa2ad12,

title = "Why protective measurement does not establish the reality of the quantum state",

abstract = "“Protective measurement” refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a “protecting” operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconstruct the quantum state in a different way via process tomography. Our second argument is based on exact analyses of special cases of protective measurement, and our final argument is to construct explicit “휓-epistemic” toy models for protective measurement, which strongly suggest that protective measurement does not imply the reality of the quantum state. The common theme of the three arguments is that almost all of the information comes from the “protection” operation rather than the quantum state of the system, and hence the schemes have no implications for the reality of the quantum state.",

author = "Joshua Combes and Christopher Ferrie and Leifer, {Matthew S.} and Pusey, {Matthew Fairbairn}",

note = "This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy. Further copying may not be permitted; contact the publisher for details ",

year = "2017",

month = jul,

day = "14",

doi = "10.1007/s40509-017-0111-4",

language = "English",

volume = "5",

pages = "189--211",

journal = "Quantum Studies: Mathematics and Foundations",

issn = "2196-5609",

publisher = "Springer",

}

TY - JOUR

T1 - Why protective measurement does not establish the reality of the quantum state

AU - Combes, Joshua

AU - Ferrie, Christopher

AU - Leifer, Matthew S.

AU - Pusey, Matthew Fairbairn

N1 - This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

PY - 2017/7/14

Y1 - 2017/7/14

N2 - “Protective measurement” refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a “protecting” operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconstruct the quantum state in a different way via process tomography. Our second argument is based on exact analyses of special cases of protective measurement, and our final argument is to construct explicit “휓-epistemic” toy models for protective measurement, which strongly suggest that protective measurement does not imply the reality of the quantum state. The common theme of the three arguments is that almost all of the information comes from the “protection” operation rather than the quantum state of the system, and hence the schemes have no implications for the reality of the quantum state.

AB - “Protective measurement” refers to two related schemes for finding the expectation value of an observable without disturbing the state of a quantum system, given a single copy of the system that is subject to a “protecting” operation. There have been several claims that these schemes support interpreting the quantum state as an objective property of a single quantum system. Here we provide three counter-arguments, each of which we present in two versions tailored to the two different schemes. Our first argument shows that the same resources used in protective measurement can be used to reconstruct the quantum state in a different way via process tomography. Our second argument is based on exact analyses of special cases of protective measurement, and our final argument is to construct explicit “휓-epistemic” toy models for protective measurement, which strongly suggest that protective measurement does not imply the reality of the quantum state. The common theme of the three arguments is that almost all of the information comes from the “protection” operation rather than the quantum state of the system, and hence the schemes have no implications for the reality of the quantum state.

U2 - 10.1007/s40509-017-0111-4

DO - 10.1007/s40509-017-0111-4

M3 - Article

SN - 2196-5609

VL - 5

SP - 189

EP - 211

JO - Quantum Studies: Mathematics and Foundations

JF - Quantum Studies: Mathematics and Foundations

ER -