Uncertainty relations based on the $ρ$-absolute variance for quantum channels

• URL: http://arxiv.org/abs/2404.08304v1
• Date: Fri, 12 Apr 2024 07:51:54 GMT
• Title: Uncertainty relations based on the $ρ$-absolute variance for quantum channels
• Authors: Cong Xu, Wen Zhou, Qing-Hua Zhang, Shao-Ming Fei,
• Abstract summary: Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. We introduce the uncertainty of quantum channels and explore its properties. The summation form of the uncertainty inequalities based on the $rho$-absolute variance for arbitrary $N$ quantum channels are also investigated and the optimal lower bounds are presented.
• Score: 7.363028199494752
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 are also investigated and the optimal lower bounds are presented. We illustrate our results by several typical examples.

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