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Entropic uncertainty and measurement reversibility

Berta, Mario and Wehner, Stephanie and Wilde, Mark M. (2016) Entropic uncertainty and measurement reversibility. New Journal of Physics, 18 (7). Art. No. 073004. ISSN 1367-2630. doi:10.1088/1367-2630/18/7/073004.

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The entropic uncertainty relation with quantum side information (EUR-QSI) from (Berta et al 2010 Nat. Phys. 6 659) is a unifying principle relating two distinctive features of quantum mechanics: quantum uncertainty due to measurement incompatibility, and entanglement. In these relations, quantum uncertainty takes the form of preparation uncertainty where one of two incompatible measurements is applied. In particular, the 'uncertainty witness' lower bound in the EUR-QSI is not a function of a post-measurement state. An insightful proof of the EUR-QSI from (Coles et al 2012 Phys. Rev. Lett. 108 210405) makes use of a fundamental mathematical consequence of the postulates of quantum mechanics known as the non-increase of quantum relative entropy under quantum channels. Here, we exploit this perspective to establish a tightening of the EUR-QSI which adds a new state-dependent term in the lower bound, related to how well one can reverse the action of a quantum measurement. As such, this new term is a direct function of the post-measurement state and can be thought of as quantifying how much disturbance a given measurement causes. Our result thus quantitatively unifies this feature of quantum mechanics with the others mentioned above. We have experimentally tested our theoretical predictions on the IBM quantum experience and find reasonable agreement between our predictions and experimental outcomes.

Item Type:Article
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URLURL TypeDescription Paper
Berta, Mario0000-0002-0428-3429
Wilde, Mark M.0000-0002-3916-4462
Additional Information:© 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 16 March 2016; Accepted 20 June 2016; Published 6 July 2016. The authors acknowledge discussions with Siddhartha Das, Michael Walter, and Andreas Winter. We are grateful to the team at IBM and the IBM Quantum Experience project. This work does not reflect the views or opinions of IBM or any of its employees. MB acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028). Additional funding support was provided by the ARO grant for Research on Quantum algorithms at the IQIM (W911NF-12-1-0521). SW acknowledges support from STW, Netherlands and an NWO VIDI Grant. MMW is grateful to SW and her group for hospitality during a research visit to QuTech in May 2015 and acknowledges support from startup funds from the Department of Physics and Astronomy at LSU, the NSF under Award No. CCF-1350397, and the DARPA Quiness Program through US Army Research Office award W31P4Q-12-1-0019.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF-12500028
Army Research Office (ARO)W911NF-12-1-0521
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
Louisiana State UniversityUNSPECIFIED
Army Research Office (ARO)W31P4Q-12-1-0019
Subject Keywords:uncertainty principle, quantum relative entropy, measurement reversibility
Issue or Number:7
Record Number:CaltechAUTHORS:20160328-110406516
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Official Citation:Mario Berta et al 2016 New J. Phys. 18 073004
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65706
Deposited By: Tony Diaz
Deposited On:30 Mar 2016 20:21
Last Modified:12 Jul 2022 19:41

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