Tightening the entropic uncertainty bound in the presence of quantum memory

Abstract

The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be expressed in terms of entropic measures. Berta \emph{et al}. [\href{http://www.nature.com/doifinder/10.1038/nphys1734}{ Nature Phys. 6, 659 (2010) }] have indicated that uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this article, we obtain a lower bound for entropic uncertainty in the presence of a quantum memory by adding an additional term depending on Holevo quantity and mutual information. We conclude that our lower bound will be tighten with respect to that of Berta \emph{et al.}, when the accessible information about measurements outcomes is less than the mutual information of the joint state. Some examples have been investigated for which our lower bound is tighter than the Berta's \emph{et al.} lower bound. Using our lower bound, a lower bound for the entanglement of formation of bipartite quantum states has obtained, as well as an upper bound for the regularized distillable common randomness.

6 pages, 1 figure to appear in PRA 2016

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• Holevo Bound of Entropic Uncertainty in Schwarzschild Spacetime
• Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations
• Experimental investigation of entropic uncertainty relations and coherence uncertainty relations
• Computing return times or return periods with rare event algorithms
• Multipartite steering inequalities based on entropic uncertainty relations
• Tightening the tripartite quantum memory assisted entropic uncertainty relation
• Reducing the entropic uncertainty lower bound in the presence of quantum memory via local operation and classical communication
• Tight entropic uncertainty relations for systems with dimension three to five
• Entropic uncertainty relations in Schwarzschild space-time
• Controlling the entropic uncertainty lower bound in two-qubit systems under the decoherence
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• Entropic uncertainty relations with quantum memory in a multipartite scenario
• Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole
• Uncertainty under Quantum Measures and Quantum Memory
• Spectral properties of the trap model on sparse networks
• Holevo bound of entropic uncertainty relation under Unruh channel in the context of open quantum systems
• Entropic uncertainty and quantum non-classicality of Unruh-Dewitt detectors in relativity
• Tripartite measurement uncertainty in Schwarzschild space-time
• Tighter sum uncertainty relations via variance and Wigner-Yanase skew information for N incompatible observables
• Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector
• Entanglement and entropy uncertainty in black hole quantum atmosphere
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
• Optimal upper bound of entropic uncertainty relation for mutually unbiased bases
• Average of uncertainty-product for bounded observables
• Tightening the entropic uncertainty relations with quantum memory in a multipartite scenario
• Entropic time-energy uncertainty relations: An algebraic approach
• Multi-point nonequilibrium umbrella sampling and associated fluctuation relations
• Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole
• Quantumness and entropic uncertainty for a pair of static Unruh-DeWitt detectors
• Characterization of the measurement uncertainty dynamics in an open system
• Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases