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<p>Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{tr}(A+B) - \textrm{tr}|A-B|\le 2\, \textrm{tr}\big (f(A)g(B)\big )\)</EquationSource> </InlineEquation> holds for every positive-valued matrix monotone function <i>f</i>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(g(x)=x/f(x)\)</EquationSource> </InlineEquation>, and all positive definite matrices <i>A</i> and <i>B</i>. In this paper, we study a new class of functions that satisfy the aforementioned inequality. As a consequence, we introduce a new quantum Chernoff bound. In addition, we characterize matrix decreasing functions and establish matrix Powers–Størmer type inequalities for perspective functions.</p>

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Revisiting Quantum Chernoff Bound and Perspective Functions

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Mohsen Kian,
  • Trung Hoa Dinh,
  • Mohammad Sal Moslehian,
  • Hiroyuki Osaka

摘要

Relating to finding possible upper bounds for the probability of error for discriminating between two quantum states, it is well-known that \(\textrm{tr}(A+B) - \textrm{tr}|A-B|\le 2\, \textrm{tr}\big (f(A)g(B)\big )\) holds for every positive-valued matrix monotone function f, where \(g(x)=x/f(x)\) , and all positive definite matrices A and B. In this paper, we study a new class of functions that satisfy the aforementioned inequality. As a consequence, we introduce a new quantum Chernoff bound. In addition, we characterize matrix decreasing functions and establish matrix Powers–Størmer type inequalities for perspective functions.