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<p>The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this paper, we introduce natural probability distributions for covariant quantum channels. Specifically, this is achieved through the application of “twirling operations” on random quantum channels derived from the Stinespring representation that uses Haar-distributed random isometries. We explore various types of group symmetries, including unitary and orthogonal covariance, hyperoctahedral covariance, and diagonal orthogonal covariance (DOC), and analyze their properties related to quantum entanglement based on the model parameters. In particular, we discuss the threshold phenomenon for positive partial transpose and entanglement breaking properties, comparing thresholds among different classes of random covariant channels. Finally, we contribute to the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\hbox {PPT}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>PPT</mtext> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> conjecture by showing that the composition between two random DOC channels is generically entanglement breaking.</p>

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Random Covariant Quantum Channels

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月26日

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  • Ion Nechita,
  • Sang-Jun Park

摘要

The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this paper, we introduce natural probability distributions for covariant quantum channels. Specifically, this is achieved through the application of “twirling operations” on random quantum channels derived from the Stinespring representation that uses Haar-distributed random isometries. We explore various types of group symmetries, including unitary and orthogonal covariance, hyperoctahedral covariance, and diagonal orthogonal covariance (DOC), and analyze their properties related to quantum entanglement based on the model parameters. In particular, we discuss the threshold phenomenon for positive partial transpose and entanglement breaking properties, comparing thresholds among different classes of random covariant channels. Finally, we contribute to the \(\hbox {PPT}^2\) PPT 2 conjecture by showing that the composition between two random DOC channels is generically entanglement breaking.