Quantum decimation in Hilbert space: Coarse graining without structure

Singh, Ashmeet; Carroll, Sean M.

doi:10.1103/PhysRevA.97.032111

Quantum decimation in Hilbert space: Coarse graining without structure

Journal Article · Wed Mar 14 00:00:00 EDT 2018 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.97.032111· OSTI ID:1597497

Singh, Ashmeet ^[1]; Carroll, Sean M. ^[2]

California Inst. of Technology (CalTech), Pasadena, CA (United States); Caltech
California Inst. of Technology (CalTech), Pasadena, CA (United States)

We introduce 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 method 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.

View Accepted Manuscript (DOE)

Research Organization:: California Inst. of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0011632

OSTI ID:: 1597497

Alternate ID(s):: OSTI ID: 1540674
OSTI ID: 1426014

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 3 Vol. 97; ISSN PLRAAN; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Quantum Coarse-Graining, Symmetries and Reducibility of Dynamics Kabernik, Oleg arXiv https://doi.org/10.48550/arxiv.1801.09770	text	January 2018

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