Universität zu Köln

Huber, Felix and Grassl, Markus ORCID: 0000-0002-3720-5195 (2020). Quantum Codes of Maximal Distance and Highly Entangled Subspaces. Quantum, 4. WIEN: VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF. ISSN 2521-327X

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Abstract

We present new bounds on the existence of general quantum maximum distance separable codes (QMDS): the length n of all QMDS codes with local dimension D and distance d >= 3 is bounded by n <= D-2 + d - 2. We obtain their weight distribution and present additional bounds that arise from Rains' shadow inequalities. Our main result can be seen as a generalization of bounds that are known for the two special cases of stabilizer QMDS codes and absolutely maximally entangled states, and confirms the quantum MDS conjecture in the special case of distance-three codes. As the existence of QMDS codes is linked to that of highly entangled subspaces (in which every vector has uniform r-body marginals) of maximal dimension, our methods directly carry over to address questions in multipartite entanglement.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Huber, Felix UNSPECIFIED UNSPECIFIED UNSPECIFIED Grassl, Markus UNSPECIFIED orcid.org/0000-0002-3720-5195 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-329780
Journal or Publication Title:	Quantum
Volume:	4
Date:	2020
Publisher:	VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF
Place of Publication:	WIEN
ISSN:	2521-327X
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MINIMUM DISTANCE; ERROR-CORRECTION; STABILIZER CODES; MDS CODES; BOUNDS Multiple languages Quantum Science & Technology; Physics, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/32978