Quantum entropy in terms of local quantum Bernoulli noises and related properties
Qi Han, Zhihe Chen, Ziqiang Lu
Abstract
Localization of quantum Bernoulli noises (LQBNs) are the family of local annihilation and local creation operators acting on Bernoulli functionals. In this paper, we construct a density operator ρk represented by LQBNs, and define a new quantum entropy S(ρk) based on LQBNs. Furthermore, we demonstrate that this quantum entropy S(ρk) also has the basic properties of von Neumann entropy, such as concavity, subadditivity, and nonnegativity. In particular, we obtain the necessary and sufficient condition for S(ρk)=k.
Topics & Concepts
Von Neumann entropyBernoulli's principleQuantum relative entropyGeneralized relative entropyQuantumQuantum discordMathematicsBernoulli schemeQuantum mutual informationEntropy (arrow of time)Joint quantum entropySubadditivityBernoulli processStatistical physicsConditional entropyQuantum operationOperator (biology)Quantum informationPhysicsQuantum mechanicsMathematical analysisPrinciple of maximum entropyOpen quantum systemQuantum entanglementThermodynamicsStatisticsTranscription factorBiochemistryChemistryGeneRepressorAdvanced Thermodynamics and Statistical MechanicsQuantum Mechanics and ApplicationsQuantum Information and Cryptography