Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases

Abstract

Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for complete sets of mutually unbiased bases in multipartite scenarios. We present lower and upper bounds of the quantum uncertainties based on the complementarity of the observables, the purity of the measured state, the (conditional) von-Neumann entropies, the Holevo quantities and mutual information. The results are illustrated by several representative cases, showing that our bounds are tighter than and outperform previously existing bounds.

References in corpus (31)

• Advances in Quantum Metrology
• The Uncertainty Principle in the Presence of Quantum Memory
• Entropic Uncertainty Relations and their Applications
• EPR Steering Inequalities from Entropic Uncertainty Relations
• Experimental non-classicality of an indivisible quantum system
• Conjectured Strong Complementary Information Tradeoff
• Experimental investigation of the uncertainty principle in the presence of quantum memory
• Experimental investigation of the entanglement-assisted entropic uncertainty principle
• 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
• Unconditional security from noisy quantum storage
• Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory
• Tightening the entropic uncertainty bound in the presence of quantum memory
• Entropic uncertainty relations for multiple measurements
• Competitions between quantum correlations in the quantum-memory-assisted entropic uncertainty relation
• Improved tripartite uncertainty relation with quantum memory
• Three ways to look at mutually unbiased bases
• Entanglement sampling and applications
• State-independent experimental tests of quantum contextuality in a three dimensional system
• Information theoretic treatment of tripartite systems and quantum channels
• Optimized entropic uncertainty relations for multiple measurements
• An equality between entanglement and uncertainty
• Strong entropic uncertainty relations for multiple measurements
• Experimental investigation of entropic uncertainty relations and coherence uncertainty relations
• Tightening the tripartite quantum memory assisted entropic uncertainty relation
• Entropic uncertainty relations in Schwarzschild space-time
• Improved quantum entropic uncertainty relations
• Entropic uncertainty relations with quantum memory in a multipartite scenario
• Uncertainty Relations in the Presence of Quantum Memory for Mutually Unbiased Measurements
• Tightening the entropic uncertainty relations with quantum memory in a multipartite scenario