Scholarlink

<p>Since a quantum ensemble generally consists of a set of mixed states, it is necessary to extend the concept of a Gram matrix to the case of mixed states. By employing two prominent alternative quantum fidelities of overlap between mixed states, the operator fidelity in terms of their Hilbert–Schmidt inner product and their purity and the super-fidelity as an upper bound for the Uhlmann–Jozsa fidelity, we introduce two important versions of Gram matrices for mixed-state ensembles. We investigate these two Gram matrices and reveal their fundamental properties; it is remarkable that they both can be regarded as quantum states. We further employ coherence of the Gram matrix which can be regarded as a quantum state to quantify quantumness contained in the ensemble. In particular, we propose to use the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(l_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-norm of coherence and the skew information of coherence, of the above Gram matrices, as several significant quantumness quantifiers. We illustrate the validity of these quantumness quantifiers by calculating them for several important ensembles generated by quantum cryptography and quantum measurement and further compare the proposed quantifiers with various existing quantities of quantumness in the literature.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quantifying the quantumness of mixed-state ensembles via fidelity

  • 期刊论文

  • 发表日期：

    2025年6月23日

查看全文
  • Meng Zhang,
  • Yajing Fan

摘要

Since a quantum ensemble generally consists of a set of mixed states, it is necessary to extend the concept of a Gram matrix to the case of mixed states. By employing two prominent alternative quantum fidelities of overlap between mixed states, the operator fidelity in terms of their Hilbert–Schmidt inner product and their purity and the super-fidelity as an upper bound for the Uhlmann–Jozsa fidelity, we introduce two important versions of Gram matrices for mixed-state ensembles. We investigate these two Gram matrices and reveal their fundamental properties; it is remarkable that they both can be regarded as quantum states. We further employ coherence of the Gram matrix which can be regarded as a quantum state to quantify quantumness contained in the ensemble. In particular, we propose to use the \(l_1\) l 1 -norm of coherence and the skew information of coherence, of the above Gram matrices, as several significant quantumness quantifiers. We illustrate the validity of these quantumness quantifiers by calculating them for several important ensembles generated by quantum cryptography and quantum measurement and further compare the proposed quantifiers with various existing quantities of quantumness in the literature.