Min- and Max-Entropy in Infinite Dimensions

Details Min- and Max-Entropy in Infinite Dimensions Min- and Max-Entropy in Infinite Dimensions

2010-04-08

arxiv.org/abs/1004.1386v2

Communications in Mathematical Physics, Vol. 306, No. 1, 165-186 (2011)

Physics

Quantum Physics

Scientific paper

10.1007/s00220-011-1282-1

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.

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