The quantum uncertainty relations of quantum channels

Abstract

The uncertainty relation reveals the intrinsic difference between the classical world and the quantum world. We investigate the quantum uncertainty relation of quantum channel in qubit systems. Under two general measurement bases, we first derive the quantum uncertainty relation for quantum channels with respect to the relative entropy of coherence. Then we obtain the quantum uncertainty relation for unitary channels with respect to the $l_1$ norm of coherence. Some examples are given in detail.

References in corpus (19)

• Advances in Quantum Metrology
• Quantifying Coherence
• Quantum Coherence as a Resource
• Robustness of coherence: An operational and observable measure of quantum coherence
• Intrinsic randomness as a measure of quantum coherence
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Improved entropic uncertainty relations and information exclusion relations
• Quantum Randomness Certified by the Uncertainty Principle
• Quantum-memory-assisted entropic uncertainty principle, teleportation and entanglement witness in structured reservoirs
• Measuring Coherence with Entanglement Concurrence
• Resource Destroying Maps
• Quantum uncertainty relation using coherence
• Experimental progress on quantum coherence: detection, quantification, and manipulation
• An equality between entanglement and uncertainty
• A new coherence measure based on fidelity
• Coherence of quantum channels
• The l1 Norm of Coherence of Assistance
• Maximum Relative Entropy of Coherence for Quantum Channels
• Trade-off relations of geometric coherence

Cited by in corpus (1)

• Complementarity relations for design-structured POVMs in terms of generalized entropies of order $\alpha \in (0,2)$