On asymptotic continuity of functions of quantum states

Abstract

A useful kind of continuity of quantum states functions in asymptotic regime is so-called asymptotic continuity. In this paper we provide general tools for checking if a function possesses this property. First we prove equivalence of asymptotic continuity with so-called it robustness under admixture. This allows us to show that relative entropy distance from a convex set including maximally mixed state is asymptotically continuous. Subsequently, we consider it arrowing - a way of building a new function out of a given one. The procedure originates from constructions of intrinsic information and entanglement of formation. We show that arrowing preserves asymptotic continuity for a class of functions (so-called subextensive ones). The result is illustrated by means of several examples.

arXiv commentMinor corrections, version submitted for publication

References in corpus (14)

• Mixed State Entanglement and Quantum Error Correction
• Classical, quantum and total correlations
• Entanglement Measures and Purification Procedures
• A Thermodynamical Approach to Quantifying Quantum Correlations
• Entanglement Measures under Symmetry
• Local versus non-local information in quantum information theory: formalism and phenomena
• Capacities of Quantum Erasure Channels
• The asymptotic entanglement cost of preparing a quantum state
• Limits for entanglement measures
• The entanglement of purification
• The Uniqueness Theorem for Entanglement Measures
• Continuity bounds for entanglement
• Limits for compression of quantum information carried by ensembles of mixed states
• Classical information deficit and monotonicity on local operations

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