Uncertainty relations based on the $\rho$ -absolute variance for quantum channelsUncertainty relations based on the $$\rho $$-absolute variance for quantum channels

Cong Xu, Wen Zhou, Qinghua Zhang +1 more

arXiv:2404.08304Quantum Information ProcessingJul 25, 20241 citation

Uncertainty of quantum channels based on symmetrized ρ-absolute variance and modified Wigner-Yanase skew information

Cong Xu, Qinghua Zhang, Shao-Ming Fei

Abstract We present the uncertainty relations in terms of the symmetrized ρ -absolute variance, which generalizes the uncertainty relations for arbitrary operators (not necessarily Hermitian) to quantum channels. By employing the quantity ∣ U ρ ∣(Φ) proposed by Zhang et al (2023) Quantum Inf. Process . 22 , 456, we also establish tighter uncertainty relations for quantum channels by using the Cauchy-Schwarz inequality. Detailed examples are provided to illustrate the tightness of our results.Abstract We present the uncertainty relations in terms of the symmetrized ρ -absolute variance, which generalizes the uncertainty relations for arbitrary operators (not necessarily Hermitian) to quantum channels. By employing the quantity ∣ U ρ ∣(Φ) proposed by Zhang et al (2023) Quantum Inf. Process . 22 , 456, we also establish tighter uncertainty relations for quantum channels by using the Cauchy-Schwarz inequality. Detailed examples are provided to illustrate the tightness of our results.

arXiv:2406.09157Physica ScriptaSep 18, 20242 citations

The quantum uncertainty relations of quantum channels

Shi-Yun Kong, Ming‐Jing Zhao, Zhi‐Xi Wang +1 more

arXiv:2408.09082Quantum Information ProcessingAug 16, 20241 citation

A note on uncertainty relations of arbitrary N quantum channels

Qinghua Zhang, Jing-Feng Wu, Shao-Ming Fei

Abstract Uncertainty principle plays a vital role in quantum physics. The Wigner–Yanase skew information characterizes the uncertainty of an observable with respect to the measured state. We generalize the uncertainty relations for two quantum channels to arbitrary N quantum channels based on Wigner–Yanase skew information. We illustrate that these uncertainty inequalities are tighter than the existing ones by detailed examples. Especially, we also discuss the uncertainty relations for N unitary channels, which could be regarded as variance-based sum uncertainty relations with respect to any pure state.Abstract Uncertainty principle plays a vital role in quantum physics. The Wigner–Yanase skew information characterizes the uncertainty of an observable with respect to the measured state. We generalize the uncertainty relations for two quantum channels to arbitrary N quantum channels based on Wigner–Yanase skew information. We illustrate that these uncertainty inequalities are tighter than the existing ones by detailed examples. Especially, we also discuss the uncertainty relations for N unitary channels, which could be regarded as variance-based sum uncertainty relations with respect to any pure state.

arXiv:2109.01345Laser Physics LettersAug 31, 202118 citations

The uncertainty relation for quantum channels based on skew information

Nan Zhou, Ming‐Jing Zhao, Zhen Wang +1 more

Quantum Information ProcessingDec 6, 20228 citations

Correlation and Information in Quantum Channels

Masashi Ban

International Journal of Theoretical PhysicsFeb 1, 20041 citation

Uncertainty relations based on the

\rho

-absolute variance for quantum channels