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Deconstruction and conditional erasure of quantum correlations

Berta, Mario and Brandão, Fernando G. S. L. and Majenz, Christian and Wilde, Mark M. (2018) Deconstruction and conditional erasure of quantum correlations. Physical Review A, 98 (4). Art. No. 042320. ISSN 2469-9926. http://resolver.caltech.edu/CaltechAUTHORS:20170726-092810091

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Abstract

We define the deconstruction cost of a tripartite quantum state on systems ABE as the minimum rate of noise needed to apply to the AE systems, such that there is negligible disturbance to the marginal state on the BE systems, while the system A of the resulting state is locally recoverable from the E system alone. We refer to such actions as deconstruction operations and protocols implementing them as state deconstruction protocols. State deconstruction generalizes Landauer erasure of a single-party quantum state as well the erasure of correlations of a two-party quantum state. We find that the deconstruction cost of a tripartite quantum state on systems ABE is equal to its conditional quantum mutual information (CQMI) I(A;B|E), thus giving the CQMI an operational interpretation in terms of a state deconstruction protocol. We also define a related task called conditional erasure, in which the goal is to apply noise to systems AE in order to decouple system A from systems BE, while causing negligible disturbance to the marginal state of systems BE. We find that the optimal rate of noise for conditional erasure is also equal to the CQMI I(A;B|E). State deconstruction and conditional erasure lead to operational interpretations of the quantum discord and squashed entanglement, which are quantum correlation measures based on the CQMI. We find that the quantum discord is equal to the cost of simulating einselection, the process by which a quantum system interacts with an environment, resulting in selective loss of information in the system. The squashed entanglement is equal to half the minimum rate of noise needed for deconstruction and/or conditional erasure if Alice has available the best possible system E to help in the deconstruction and/or conditional erasure task.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevA.98.042320DOIArticle
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.042320PublisherArticle
https://arxiv.org/abs/1609.06994arXivDiscussion Paper
ORCID:
AuthorORCID
Berta, Mario0000-0002-0428-3429
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2018 American Physical Society. Received 8 August 2018; published 15 October 2018. We are indebted to Siddhartha Das, Gilad Gour, Matt Hastings, Mio Murao, Marco Piani, Kaushik Seshadreesan, Eyuri Wakakuwa, and Andreas Winter for valuable discussions. We also acknowledge the catalyzing role of the open problems session at Beyond IID 2016, which ultimately led to the solution of the i.i.d result presented here. M.B. acknowledges funding by the SNSF through a fellowship, funding by the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (NFS Grant No. PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028), and funding support from the ARO grant for Research on Quantum Algorithms at the IQIM (No. W911NF-12-1-0521). C.M. acknowledges financial support from the European Research Council (ERC Grant Agreement No. 337603), the Danish Council for Independent Research (Sapere Aude) and VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059). M.M.W. acknowledges support from the NSF under Award No. CCF-1350397.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
Army Research Office (ARO)W911NF-12-1-0521
European Research Council (ERC)337603
Danish Council for Independent ResearchUNSPECIFIED
Villum Foundation10059
NSFCCF-1350397
Record Number:CaltechAUTHORS:20170726-092810091
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170726-092810091
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79401
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 Jul 2017 22:39
Last Modified:16 Oct 2018 18:40

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