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arXiv:1906.06209 · Electronic Journal of Linear Algebra

A Note on Parallel Distinguishability of two Quantum Operations

Chi-Kwong Li, Yue Liu, Chao Ma, Diane Christine Pelejo

Published Apr 14, 2020• 0 citations
arXivHTMLPDF

Abstract

In this work, the authors consider a homogeneous system of linear equations of the form $A_\alpha^{\otimes N} \mathbf{x} = 0$ arising from the distinguishability of two quantum operations by $N$ uses in parallel, where the coefficient matrix $A_\alpha$ depends on a real parameter $\alpha$. It was conjectured by Duan et al. that the system has a non-trivial nonnegative solution if and only if $\alpha$ lies in a certain interval $R_N$ depending on $N$. The authors affirm the necessity part of the conjecture and establish the sufficiency of the conjecture for $N\leq 10$ by presenting explicit non-trivial nonnegative solutions for the linear system.

DOI
10.13001/ela.2020.4957

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