Quantum-memory-assisted entropic uncertainty relations

Abstract

Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the uncertainty principle, entropy-based uncertainty relations lead to a number of applications including quantum key distribution, entanglement witness, quantum steering, quantum metrology, and quantum teleportation. Herein, the history of the development of the uncertainty relations is discussed, especially focusing on the recent progress with regard to quantum-memory-assisted entropic uncertainty relations and dynamical characteristics of the measured uncertainty in some explicit physical systems. The aims are to help deepen the understanding of entropic uncertainty relations and prompt further explorations for versatile applications of the relations on achieving practical quantum tasks.

Review, 20 pages, published in Ann. Phys. (Berlin)

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Cited by in corpus (18)

• Improved tripartite uncertainty relation with quantum memory
• Optimized entropic uncertainty relations for multiple measurements
• Experimental investigation of entropic uncertainty relations and coherence uncertainty relations
• The Generalized Uncertainty Principle
• Sequential sharing of two-qudit entanglement based on the entropic uncertainty relation
• Unification of quantum resources in tripartite systems
• Quantum-information theory of magnetic field influence on circular dots with different boundary conditions
• Rényi and Tsallis entropies of the Dirichlet and Neumann one-dimensional quantum wells
• One-dimensional pseudoharmonic oscillator: classical remarks and quantum-information theory
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
• An improved bound for strong unitary uncertainty relations with refined sequence
• Quantum information measures of the Dirichlet and Neumann hyperspherical dots
• Multiple uncertainty relation for accelerated quantum information
• Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field
• Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole
• Experimental test of the majorization uncertainty relation with mixed states
• Entropic uncertainty and coherence in Einstein-Gauss-Bonnet gravity
• Entropic uncertainty under indefinite causal order and input-output direction