Singleton bounds for entanglement-assisted classical and quantum error correcting codes

We show that entirely information theoretic methods, based on von Neumann entropies and their properties, can be used to derive Singleton bounds on the performance of entanglement-assisted hybrid classical-quantum (EACQ) error correcting codes. Concretely we show that the triple-rate region of qubit...

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Main Authors: Mamindlapally, Manideep, Winter, Andreas
Format: Conference Proceeding
Language:English
Subjects:
Entropy
Error correction codes
Hilbert space
Quantum entanglement
Qubit
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Winter, Andreas
description We show that entirely information theoretic methods, based on von Neumann entropies and their properties, can be used to derive Singleton bounds on the performance of entanglement-assisted hybrid classical-quantum (EACQ) error correcting codes. Concretely we show that the triple-rate region of qubits, cbits and ebits of possible EACQ codes over arbitrary alphabet sizes is contained in the quantum Shannon theoretic rate region of an associated memoryless erasure channel, which turns out to be a polytope. We show that a large part of this region is attainable by certain EACQ codes, whenever the local alphabet size (i.e. Hilbert space dimension) is large enough, in keeping with known facts about classical and quantum minimum distance separable (MDS) codes: in particular all of its extreme points and several important extremal lines. Full details in [1].
doi_str_mv 10.1109/ISIT50566.2022.9834561
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subjects Entropy
Error correction codes
Hilbert space
Quantum entanglement
Qubit
title Singleton bounds for entanglement-assisted classical and quantum error correcting codes
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