Universität zu Köln

Aragones-Soria, Y., Aberg, J., Park, C-Y and Kastoryano, M. J. (2021). Classical restrictions of generic matrix product states are quasi-locally Gibbsian. J. Math. Phys., 62 (9). MELVILLE: AIP Publishing. ISSN 1089-7658

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Abstract

We show that norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states of local Hamiltonians (i.e., they are quasi-locally Gibbsian) if the classical conditional mutual information (CMI) of any connected tripartition of the lattice is rapidly decaying in the width of the middle region. For injective matrix product states, we, moreover, show that the classical CMI decays exponentially whenever the collection of matrix product operators satisfies a purity condition, a notion previously established in the theory of random matrix products. We, furthermore, show that violation of the purity condition enables a generalized notion of error correction on the virtual space, thus indicating the non-generic nature of such violations. We make this intuition more concrete by constructing a probabilistic model where purity is a typical property. The proof of our main result makes extensive use of the theory of random matrix products and may find applications elsewhere. Published under an exclusive license by AIP Publishing

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Aragones-Soria, Y. UNSPECIFIED UNSPECIFIED UNSPECIFIED Aberg, J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Park, C-Y UNSPECIFIED UNSPECIFIED UNSPECIFIED Kastoryano, M. J. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-573145
DOI:	10.1063/5.0040256
Journal or Publication Title:	J. Math. Phys.
Volume:	62
Number:	9
Date:	2021
Publisher:	AIP Publishing
Place of Publication:	MELVILLE
ISSN:	1089-7658
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language QUANTUM; DENSITY Multiple languages Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/57314