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引用次数: 0
摘要
不确定性原理揭示了经典世界与量子世界的内在差异,在量子信息论中发挥着重要作用。通过使用(\rho \)绝对方差,我们引入了量子信道的不确定性,并探讨了它的性质。利用考希-施瓦茨不等式和平行四边形定律,我们分别建立了任意两个量子信道的不确定性关系的乘积形式和求和形式。我们还研究了任意 N 个量子信道基于 \(\rho \)-绝对方差的不确定性不等式的求和形式,并给出了最优下限。我们通过几个典型的例子来说明我们的结果。
Uncertainty relations based on the \(\rho \)-absolute variance for quantum channels
Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. By using \(\rho \)-absolute variance, we introduce the uncertainty of quantum channels and explore its properties. By using Cauchy–Schwarz inequality and the parallelogram law, we establish the product and summation forms of the uncertainty relations for arbitrary two quantum channels, respectively. The summation form of the uncertainty inequalities based on the \(\rho \)-absolute variance for arbitrary N quantum channels is also investigated, and the optimal lower bounds are presented. We illustrate our results by several typical examples.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.