Albert, Victor V. (2019) Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states. Quantum, 3 . Art. No. 151. ISSN 2521-327X. doi:10.22331/q-2019-06-06-151. https://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 formula stems from a Noether-like theorem stating that, for any channel admitting a full-rank fixed point, conserved quantities commute with that channel’s Kraus operators up to a phase. The formula is applied to adiabatic transport of the fixed-point space of channels, revealing cases where the dissipative/spectral gap can close during any segment of the adiabatic path. The formula is also applied to calculate expectation values of noninjective matrix product states (MPS) in the thermodynamic limit, revealing that those expectation values can also be calculated using an MPS with reduced bond dimension and a modified boundary.
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| Alternate Title: | Asymptotics of quantum channels: application to matrix product states | |||||||||
| Additional Information: | © 2019 This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. Published: 2019-06-06. Insightful discussions with B. Bradlyn, X. Chen, M. Fraas, L. Jiang, D. Perez-Garcia, M. B. Sahinoglu, N. Schuch, F. Ticozzi, A. M. Turner, and M. M. Wolf are acknowledged. This research was supported in part by the National Science Foundation (PHY17-48958) 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: | Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics | |||||||||
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| DOI: | 10.22331/q-2019-06-06-151 | |||||||||
| Record Number: | CaltechAUTHORS:20190208-122111876 | |||||||||
| Persistent URL: | https://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: | 16 Nov 2021 03:53 |
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