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<p>Quantum cross entropy is a measure of information that quantifies the difference between two quantum states. In this paper, we first define the local quantum cross entropy based on local quantum Bernoulli noises (LQBNs) and examine several of its relevant properties, including its relationships with local quantum entropy and local quantum relative entropy, as well as its non-negativity, asymmetry, monotonicity, and unitary invariance with respect to the second parameter. Then, we investigate the local quantum cross entropy between any local quantum state and the normalized identity operator. Finally, we research its application in local quantum data compression.</p>

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Local Quantum Cross Entropy and its Properties

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Qi Han,
  • Lijie Gou

摘要

Quantum cross entropy is a measure of information that quantifies the difference between two quantum states. In this paper, we first define the local quantum cross entropy based on local quantum Bernoulli noises (LQBNs) and examine several of its relevant properties, including its relationships with local quantum entropy and local quantum relative entropy, as well as its non-negativity, asymmetry, monotonicity, and unitary invariance with respect to the second parameter. Then, we investigate the local quantum cross entropy between any local quantum state and the normalized identity operator. Finally, we research its application in local quantum data compression.