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Asymptotics of quantum channels: application to matrix product states

Albert, Victor V. (2018) Asymptotics of quantum channels: application to matrix product states. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20190208-122111876

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Abstract

This work derives an analytical formula for the asymptotic state -- the quantum state resulting from an infinite number of applications of a general quantum channel on some initial state. For channels admitting multiple fixed or rotating points, conserved quantities -- the left fixed/rotating points of the channel -- determine the dependence of the asymptotic state on the initial state. The analytical formula stems from results regarding conserved quantities, including the fact that, for any channel admitting a full-rank fixed point, conserved quantities commute with that channel's Kraus operators up to a phase. In the same way that asymptotic states depend on initial states, the thermodynamic limit of (noninjective) matrix product states (MPS) depends on the MPS boundary conditions. Expectation values of local observables in such MPS are calculated in the thermodynamic limit, showing that effects due to the interaction of "twisted" boundary conditions with decaying bond degrees of freedom can persist. It is shown that one can eliminate all decaying bond degrees of freedom and calculate the same expectation values using mixtures of MPS with reduced bond dimension and multiple boundary conditions.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1803.00109arXivDiscussion Paper
Additional Information:Insightful discussions with L. Jiang, M. Fraas, N. Schuch, M. M. Wolf, D. Perez-Garcia, M. B. Sahinoglu, A. M. Turner, B. Bradlyn, F. Ticozzi, and X. Chen are acknowledged. This research was supported in part by the National Science Foundation (PHY-1748958) and the Walter Burke Institute for Theoretical Physics at Caltech. I thank KITP Santa Barbara for their hospitality as part of the Quantum Physics of Information workshop.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFPHY-1748958
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechAUTHORS:20190208-122111876
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190208-122111876
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92796
Collection:CaltechAUTHORS
Deposited By: Bonnie Leung
Deposited On:15 Feb 2019 21:09
Last Modified:15 Feb 2019 21:09

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