Quantum error-correction codes and absolutely maximally entangled states

Paweł Mazurek , Máté Farkas , Andrzej Grudka , Michał Horodecki , Michał Studziński

Abstract

For every stabilizer N-qudit absolutely maximally entangled state, we present a method for determining the stabilizer generators and logical operators of a corresponding quantum error-correction code. These codes encode k qudits into N - k qudits, with k <= left perpendicular N/2 right perpendicular, where the local dimension d is prime. We use these methods to analyze the concatenation of such quantum codes and link this procedure to entanglement swapping. Using our techniques, we investigate the spread of quantum information on a tensor network code formerly used as a toy model for the AdS/CFT correspondence. In this network, we show how corrections arise to the Ryu-Takayanagi formula in the case of entangled input state, and that the bound on the entanglement entropy of the boundary state is saturated for absolutely maximally entangled input states.
Author Paweł Mazurek (ICTQT)
Paweł Mazurek,,
- International Centre for Theory of Quantum Technologies
, Máté Farkas (FMPI/ITPA)
Máté Farkas,,
- Institute of Theoretical Physics and Astrophysics
, Andrzej Grudka
Andrzej Grudka,,
-
, Michał Horodecki (ICTQT)
Michał Horodecki,,
- International Centre for Theory of Quantum Technologies
, Michał Studziński (FMPI/ITPA)
Michał Studziński,,
- Institute of Theoretical Physics and Astrophysics
Journal seriesPhysical Review A, ISSN 2469-9926, e-ISSN 2469-9934, (N/A 100 pkt)
Issue year2020
Vol101
No4
Pages1-10
Publication size in sheets0.50
Article number042305
ASJC Classification3107 Atomic and Molecular Physics, and Optics
DOIDOI:10.1103/PhysRevA.101.042305
URL https://doi.org/10.1103/PhysRevA.101.042305
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 20-07-2020, ArticleFromJournal
Publication indicators WoS Citations = 0.000; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.886; WoS Impact Factor: 2018 = 2.907 (2) - 2018=2.723 (5)
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