Tightening the tripartite quantum memory assisted entropic uncertainty relation

Abstract

The uncertainty principle determines the distinction between the classical and quantum worlds. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum information theory, Shannon entropy has been used as an appropriate measure to express the uncertainty relation. According to the applications of entropic uncertainty relation, studying and trying to improve the bound of this relation is of great importance. Uncertainty bound can be altered by considering an extra quantum system as the quantum memory $B$ which is correlated with the measured quantum system $A$. One can extend the bipartite quantum memory assisted entropic uncertainty relation to tripartite quantum memory assisted entropic uncertainty relation in which the memory is split into two parts. In this work, we obtain a lower bound for the tripartite quantum memory assisted entropic uncertainty relation. Our lower bound has two additional terms compared to the lower bound in [Phys. Rev. Lett. 103, 020402 (2009)] which depending on the conditional von Neumann entropy, the Holevo quantity and mutual information. It is shown that the bound obtained in this work is more tighter than other bounds. In addition, using our lower bound, a lower bound for the quantum secret key rate has been obtained. The lower bound is also used to obtain the states for which the strong subadditivity inequality and Koashi-Winter inequality is satisfied with equality.

arXiv comment6 pages, 4 figures, comments and suggestions are welcome!

References in corpus (39)

• Advances in Quantum Metrology
• Distillation of secret key and entanglement from quantum states
• The Uncertainty Principle in the Presence of Quantum Memory
• Entropic Uncertainty Relations and their Applications
• Monogamy of entanglement and other correlations
• The Uncertainty Relation for Smooth Entropies
• Entropic uncertainty relations - A survey
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• EPR Steering Inequalities from Entropic Uncertainty Relations
• Conjectured Strong Complementary Information Tradeoff
• Stronger uncertainty relations for the sum of variances
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Improved entropic uncertainty relations and information exclusion relations
• Quantum Randomness Certified by the Uncertainty Principle
• Inequalities for Quantum Entropy: A Review with Conditions for Equality
• Conservation law for distributed entanglement of formation and quantum discord
• Unconditional security from noisy quantum storage
• Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory
• Entropic uncertainty relation for mutually unbiased bases
• Source-independent quantum random number generation
• Strong Majorization Entropic Uncertainty Relations
• Tightening the entropic uncertainty bound in the presence of quantum memory
• Entropic uncertainty relations for multiple measurements
• Improved tripartite uncertainty relation with quantum memory
• Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases
• Entanglement sampling and applications
• Information theoretic treatment of tripartite systems and quantum channels
• Fine-grained lower limit of entropic uncertainty in the presence of quantum memory
• Improved bounds in entropic uncertainty relations
• An equality between entanglement and uncertainty
• Quantum and classical entropic uncertainty relations
• General entropy-like uncertainty relations in finite dimensions
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Strong entropic uncertainty relations for multiple measurements
• Optimal Uncertainty Relations for Extremely Coarse-grained Measurements
• Lower bound of quantum uncertainty from extractable classical information
• Reducing the entropic uncertainty lower bound in the presence of quantum memory via local operation and classical communication
• Controlling the entropic uncertainty lower bound in two-qubit systems under the decoherence
• Reexamination of strong subadditivity: A quantum-correlation approach

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• Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
• Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases