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arXiv:quant-ph/9705037

Remarks on Bounds for Quantum Codes

Alexei Ashikhmin

Published May 21, 1997• 3 citations
arXivHTMLPDF

Abstract

We present some results that show that bounds from classical coding theory still work in many cases of quantum coding theory.
DOI
10.48550/arxiv.quant-ph/9705037

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Random access codes are a type of communication task that is widely used in quantum information science. The optimal average success probability that can be achieved through classical strategies is known for any random access code. However, only a few cases are solved exactly for quantum random access codes. In this paper, we provide bounds for the fully general setting of n independent variables, each selected from a d-dimensional classical alphabet and encoded in a D-dimensional quantum system subject to an arbitrary quantum measurement. The bound recovers the exactly known special cases, and we demonstrate numerically that even though the bound is not tight overall, it can still yield a good approximation.