Improved tripartite uncertainty relation with quantum memory

Abstract

Uncertainty principle is a striking and fundamental feature in quantum mechanics distinguishing from classical mechanics. It offers an important lower bound to predict outcomes of two arbitrary incompatible observables measured on a particle. In quantum information theory, this uncertainty principle is popularly formulized in terms of entropy. Here, we present an improvement of tripartite quantum-memory-assisted entropic uncertainty relation. The uncertainty's lower bound is derived by considering mutual information and Holevo quantity. It shows that the bound derived by this method will be tighter than the lower bound in [Phys. Rev. Lett. 103, 020402 (2009)]. Furthermore, regarding a pair of mutual unbiased bases as the incompatibility, our bound will become extremely tight for the three-qubit $\text{X}$-state system, completely coinciding with the entropy-based uncertainty, and can restore Renes $\text{et al.}$'s bound with respect to arbitrary tripartite pure states. In addition, by applying our lower bound, one can attain the tighter bound of quantum secret key rate, which is of basic importance to enhance the security of quantum key distribution protocols.

7 pages, 4 figures. Accepted by Physical Review A

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• Cutoff phenomenon and entropic uncertainty for random quantum circuits
• Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole
• Experimental test of the majorization uncertainty relation with mixed states
• Photonic Energy-Coherence Theorem and Experimental Validations
• Quantumness and entropic uncertainty for a pair of static Unruh-DeWitt detectors
• Entropic uncertainty and coherence in Einstein-Gauss-Bonnet gravity
• Identifying the $3$-qubit $W$ state with quantum uncertainty relation
• Entropic uncertainty under indefinite causal order and input-output direction
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• Quantum Uncertainty Dynamics