A note on uncertainty relations of arbitrary N quantum channels

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 comment12 pages, 2 figures

References in corpus (26)

• The capacity of the noisy quantum channel
• Entropic Uncertainty Relations and their Applications
• Quantum channels and memory effects
• Conjectured Strong Complementary Information Tradeoff
• Universal Uncertainty Relations
• Fidelity balance in quantum operations
• Majorization entropic uncertainty relations
• Entropic uncertainty relation for mutually unbiased bases
• Strong Majorization Entropic Uncertainty Relations
• Tightening the entropic uncertainty bound in the presence of quantum memory
• Entropic Uncertainty Relations in Quantum Physics
• Operational Resource Theory of Quantum Channels
• Quantifying Operations with an Application to Coherence
• Uncertainty relations for MUBs and SIC-POVMs in terms of generalized entropies
• Measuring Non-Hermitian Operators via Weak Values
• Quantifying the resource content of quantum channels: An operational approach
• Rényi entropy uncertainty relation for successive projective measurements
• Sum uncertainty relations based on Wigner-Yanase skew information
• Optimized entropic uncertainty relation for successive measurement
• Uncertainties in Successive Measurements
• Uncertainty, joint uncertainty, and the quantum uncertainty principle
• Discording power of quantum evolutions
• Measuring coherence of quantum measurements
• Tighter uncertainty relations based on Wigner-Yanase skew information for observables and channels
• Optimal Entropic Uncertainty Relation for Successive Measurements in Quantum Information Theory
• Coherence generating power of unitary transformations via probabilistic average

Cited by in corpus (12)

• Tighter sum uncertainty relations via metric-adjusted skew information
• A note on uncertainty relations of metric-adjusted skew information
• Product and sum uncertainty relations based on metric-adjusted skew information
• Sum uncertainty relations based on $(\alpha ,\beta ,\gamma )$ weighted Wigner-Yanase-Dyson skew information
• Enhanced quantum channel uncertainty relations by skew information
• Wigner-Yanase skew information-based uncertainty relations for quantum channels
• Tighter uncertainty relations based on $(\alpha ,\beta ,\gamma )$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels
• A note on Wigner-Yanase skew information-based uncertainty of quantum channels
• Uncertainty of quantum channels based on symmetrized \r{ho}-absolute variance and modified Wigner-Yanase skew information
• Mixed-permutation channel with its application to estimate quantum coherence
• Stronger sum uncertainty relations for non-Hermitian operators
• Uncertainty relations based on the $\rho$-absolute variance for quantum channels