Min- and Max-Entropy in Infinite Dimensions

Abstract

We consider an extension of the conditional min- and max-entropies to infinite-dimensional separable Hilbert spaces. We show that these satisfy characterizing properties known from the finite-dimensional case, and retain information-theoretic operational interpretations, e.g., the min-entropy as maximum achievable quantum correlation, and the max-entropy as decoupling accuracy. We furthermore generalize the smoothed versions of these entropies and prove an infinite-dimensional quantum asymptotic equipartition property. To facilitate these generalizations we show that the min- and max-entropy can be expressed in terms of convergent sequences of finite-dimensional min- and max-entropies, which provides a convenient technique to extend proofs from the finite to the infinite-dimensional setting.

References in corpus (8)

• The Uncertainty Principle in the Presence of Quantum Memory
• Quantum information can be negative
• The thermodynamic meaning of negative entropy
• Duality Between Smooth Min- and Max-Entropies
• The work value of information
• Smooth Renyi Entropies and the Quantum Information Spectrum
• Generalized relative entropies and the capacity of classical-quantum channels
• Entanglement cost in practical scenarios

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