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Quantum decimation in Hilbert space: Coarse graining without structure

Singh, Ashmeet and Carroll, Sean M. (2018) Quantum decimation in Hilbert space: Coarse graining without structure. Physical Review A, 97 (3). Art. No. 032111. ISSN 2469-9926. doi:10.1103/PhysRevA.97.032111.

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We present a technique to coarse grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred set of operators (local or otherwise) in an associated algebra. Rather, we use the data corresponding to a given set of states, either specified independently or constructed from a single state evolving in time. Our technique is based on principle component analysis (PCA), and the resulting coarse-grained quantum states live in a lower-dimensional Hilbert space whose basis is defined using the underlying (isometric embedding) transformation of the set of fine-grained states we wish to coarse grain. Physically, the transformation can be interpreted to be an “entanglement coarse-graining” scheme that retains most of the global, useful entanglement structure of each state, while needing fewer degrees of freedom for its reconstruction. This scheme could be useful for efficiently describing collections of states whose number is much smaller than the dimension of Hilbert space, or a single state evolving over time.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Singh, Ashmeet0000-0002-4404-1416
Carroll, Sean M.0000-0002-4226-5758
Additional Information:© 2018 American Physical Society. Received 6 September 2017; published 14 March 2018. We would like to thank Ning Bao, ChunJun (Charles) Cao, and Jess Riedel for helpful discussions during the course of this project. We are also thankful to an anonymous reviewer for their comments to help improve the manuscript. This material is based upon work supported by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, as well as by the Walter Burke Institute for Theoretical Physics at Caltech and the Foundational Questions Institute.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Foundational Questions Institute (FQXI)UNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20180327-074233712
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85438
Deposited By: Tony Diaz
Deposited On:27 Mar 2018 18:28
Last Modified:15 Nov 2021 20:28

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