The uncertainty of quantum states with respect to the projective measurement

Abstract

The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it systematically with respect to given projective measurement. Some basic concepts about uncertainty are reformulated in this context. We prove and get the form of the uncertainty preserving operations. The quantum states with maximal uncertainty are characterized. A universal decomposition of uncertainty into classical uncertainty and quantum uncertainty is provided. Furthermore, a unified and general relation among uncertainty, coherence and coherence of assistance is established. These results are independent of any explicit uncertainty measure. At last, we propose a new uncertainty measure called the geometric uncertainty based on the fidelity and link it with the geometric coherence.

arXiv comment15 pages

References in corpus (27)

• Quantum entanglement
• Advances in Quantum Metrology
• Quantifying Coherence
• Quantum Coherence as a Resource
• The classical-quantum boundary for correlations: discord and related measures
• Measuring Quantum Coherence with Entanglement
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Entropic Uncertainty Relations and their Applications
• The Uncertainty Relation for Smooth Entropies
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• EPR Steering Inequalities from Entropic Uncertainty Relations
• Conjectured Strong Complementary Information Tradeoff
• Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
• Assisted distillation of quantum coherence
• Quantum Randomness Certified by the Uncertainty Principle
• Universal Uncertainty Relations
• Majorization entropic uncertainty relations
• Source-independent quantum random number generation
• Measuring Coherence with Entanglement Concurrence
• Operational one-to-one mapping between coherence and entanglement measures
• Linking a distance measure of entanglement to its convex roof
• Quantum uncertainty relation using coherence
• An equality between entanglement and uncertainty
• Partial coherence and quantum correlation with fidelity and affinity distances
• The Conditional Uncertainty Principle
• Conjectured strong complementary-correlations tradeoff
• The Average Quantum Coherence of Pure State Decomposition