Advanced Alicki-Fannes-Winter method for energy-constrained quantum systems and its use

Abstract

We describe an universal method for quantitative continuity analysis of entropic characteristics of energy-constrained quantum systems and channels. It gives asymptotically tight continuity bounds for basic characteristics of quantum systems of wide class (including multi-mode quantum oscillators) and channels between such systems under the energy constraint. The main application of the proposed method is the advanced version of the uniform finite-dimensional approximation theorem for basic capacities of energy-constrained quantum channels.

arXiv comment33 pages, Section 5 contains the answer to everyone who asked me about the possibility to improve the dimension estimates in arXiv:1707.05641, in v.3 it is shown that the proposed method gives asymptotically tight continuity bounds in more general case

References in corpus (36)

• "Squashed Entanglement" - An Additive Entanglement Measure
• End-to-end capacities of a quantum communication network
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
• Continuity of quantum conditional information
• The exact cost of redistributing multipartite quantum states
• On the quantum Renyi relative entropies and related capacity formulas
• The structure of degradable quantum channels
• Approaches for approximate additivity of the Holevo information of quantum channels
• Continuity of quantum channel capacities
• Continuity bounds on the quantum relative entropy
• Approximate Degradable Quantum Channels
• Continuity bounds on the quantum relative entropy - II
• Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
• On asymptotic continuity of functions of quantum states
• Energy-constrained private and quantum capacities of quantum channels
• Tight continuity bounds for the quantum conditional mutual information, for the Holevo quantity and for capacities of quantum channels
• Asymptotic security of discrete-modulation protocols for continuous-variable quantum key distribution
• Tight bound on relative entropy by entropy difference
• Fundamental limits on key rates in device-independent quantum key distribution
• Measures of quantum correlations in infinite-dimensional systems
• Quantum conditional entropy for infinite-dimensional systems
• Distinguishability measures between ensembles of quantum states
• Convergence rates for quantum evolution & entropic continuity bounds in infinite dimensions
• Maximum and minimum entropy states yielding local continuity bounds
• Continuity bounds for information characteristics of quantum channels depending on input dimension
• Uniform continuity bounds for information characteristics of quantum channels depending on input dimension and on input energy
• Adaptation of the Alicki-Fannes-Winter method for the set of states with bounded energy and its use
• Conditional channel simulation
• Optimal uniform continuity bound for conditional entropy of classical--quantum states
• Converse bounds for quantum and private communication over Holevo-Werner channels
• Quantum Channel Capacities Per Unit Cost
• Necessary criterion for approximate recoverability
• Communication Cost for Non-Markovianity of Tripartite Quantum States: A Resource Theoretic Approach
• Quantum-capacity bounds in spin-network communication channels
• Uniform finite-dimensional approximation of basic capacities of energy-constrained channels

Cited by in corpus (13)

• Asymptotic state transformations of continuous variable resources
• Continuity of quantum entropic quantities via almost convexity
• From Classical to Quantum: Uniform Continuity Bounds on Entropies in Infinite Dimensions
• Continuity of characteristics of composite quantum systems
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Continuity bounds on observational entropy and measured relative entropies
• On quantum channels and operations preserving finiteness of the von Neumann entropy
• General Continuity Bounds for Quantum Relative Entropies
• Uniform continuity bounds for characteristics of multipartite quantum systems
• Convergence conditions for the quantum relative entropy and other applications of the deneralized quantum Dini lemma
• Continuity bounds for quantum entropies arising from a fundamental entropic inequality
• Unified framework for continuity of sandwiched Rényi divergences
• On quantum states with a finite-dimensional approximation property