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<p>This note introduces a family of circulant quantum channels — a subclass of the mixed-permutation channels — and investigates its key structural and operational properties. We show that the image of the circulant quantum channel is precisely the set of circulant matrices. This characterization facilitates the analysis of arbitrary <i>n</i>-th order Bargmann invariants. Furthermore, we prove that the channel is entanglement-breaking, implying a substantially reduced resource cost for erasing quantum correlations compared to a general mixed-permutation channel. Applications of this channel are also discussed, including the derivation of tighter lower bounds for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _p\)</EquationSource> </InlineEquation>-norm coherence and a characterization of its action in bipartite systems.</p>

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Circulant Quantum Channels and its Applications

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Bing Xie,
  • Lin Zhang

摘要

This note introduces a family of circulant quantum channels — a subclass of the mixed-permutation channels — and investigates its key structural and operational properties. We show that the image of the circulant quantum channel is precisely the set of circulant matrices. This characterization facilitates the analysis of arbitrary n-th order Bargmann invariants. Furthermore, we prove that the channel is entanglement-breaking, implying a substantially reduced resource cost for erasing quantum correlations compared to a general mixed-permutation channel. Applications of this channel are also discussed, including the derivation of tighter lower bounds for \(\ell _p\) -norm coherence and a characterization of its action in bipartite systems.