Non-binary entanglement-assisted stabilizer codes

Nadkarni, PJ and Garani, SS (2021) Non-binary entanglement-assisted stabilizer codes. In: Quantum Information Processing, 20 (8).

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Abstract

Using pre-shared entangled states between the encoder and the decoder, we provide a previously unreported coding-theoretic framework for constructing entanglement-assisted stabilizer codes over qudits of dimension pk from first principles, where p is prime and k� Z+. We introduce the concept of mathematically decomposing a qudit of dimension pk into k subqudits, each of dimension p. Our contributions toward the entanglement-assisted stabilizer coding framework over qudits are multi-fold as follows: (a) We study the properties of the code and derive an analytical expression for the minimum number of pre-shared entangled subqudits required to construct the code. (b) We provide a code construction procedure that involves obtaining the explicit form of the stabilizers of the code. (c) We show that the proposed entanglement-assisted qudit stabilizer codes are analogous to classical additive codes over Fpk. (d) We provide the quantum coding bounds, such as the quantum Hamming bound, the quantum Singleton bound, and the quantum Gilbert�Varshamov bound for non-degenerate entanglement-assisted stabilizer codes over qudits. (e) We finally demonstrate that the error correction capability of the code can be increased with entanglement assistance. The proposed framework is useful for realizing coded quantum computing and communication systems over pk-dimensional qudits. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Item Type:	Journal Article
Publication:	Quantum Information Processing
Publisher:	Springer
Additional Information:	The copyright for this article belongs to Springer
Keywords:	Codes (symbols); Error correction; Quantum computers, Analytical expressions; Classical additives; Code construction; Coding framework; Error correction capability; First principles; Quantum Computing; Stabilizer codes, Quantum entanglement
Department/Centre:	Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Date Deposited:	20 Nov 2021 11:29
Last Modified:	20 Nov 2021 11:29
URI:	http://eprints.iisc.ac.in/id/eprint/69834

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