Korzekwa, K, Jennings, D orcid.org/0000-0003-1201-3725 and Rudolph, T (2014) Operational constraints on state-dependent formulations of quantum error-disturbance trade-off relations. Physical Review A, 89 (5). ARTN 052108. ISSN 1050-2947
Abstract
We argue for an operational requirement that all state-dependent measures of disturbance should satisfy. Motivated by this natural criterion, we prove that in any d-dimensional Hilbert space and for any pair of noncommuting operators, A and B, there exists a set of at least 2d−1 zero-noise, zero-disturbance (ZNZD) states, for which the first observable can be measured without noise and the second will not be disturbed. Moreover, we show that it is possible to construct such ZNZD states for which the expectation value of the commutator [A,B] does not vanish. Therefore any state-dependent error-disturbance relation, based on the expectation value of the commutator as a lower bound, must violate the operational requirement. We also discuss Ozawa's state-dependent error-disturbance relation in light of our results and show that the disturbance measure used in this relation exhibits unphysical properties. We conclude that the trade-off is inevitable only between state-independent measures of error and disturbance.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 American Physical Society. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) > Theoretical Physics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 Jan 2019 09:33 |
Last Modified: | 04 Jan 2019 09:33 |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevA.89.052108 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:139401 |