期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 306, 期 1, 页码 165-186出版社
SPRINGER
DOI: 10.1007/s00220-011-1282-1
关键词
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资金
- Leibniz University Hannover [Graduiertenkolleg 1463]
- Swiss National Science Foundation [200021-119868]
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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