124 research outputs found
Smooth Renyi Entropies and the Quantum Information Spectrum
Many of the traditional results in information theory, such as the channel
coding theorem or the source coding theorem, are restricted to scenarios where
the underlying resources are independent and identically distributed (i.i.d.)
over a large number of uses. To overcome this limitation, two different
techniques, the information spectrum method and the smooth entropy framework,
have been developed independently. They are based on new entropy measures,
called spectral entropy rates and smooth entropies, respectively, that
generalize Shannon entropy (in the classical case) and von Neumann entropy (in
the more general quantum case). Here, we show that the two techniques are
closely related. More precisely, the spectral entropy rate can be seen as the
asymptotic limit of the smooth entropy. Our results apply to the quantum
setting and thus include the classical setting as a special case
General theory of environment-assisted entanglement distillation
We evaluate the one-shot entanglement of assistance for an arbitrary
bipartite state. This yields another interesting result, namely a
characterization of the one-shot distillable entanglement of a bipartite pure
state. This result is shown to be stronger than that obtained by specializing
the one-shot hashing bound to pure states. Finally, we show how the one-shot
result yields the operational interpretation of the asymptotic entanglement of
assistance proved in [Smolin et al., Phys. Rev. A 72, 052317 (2005)].Comment: 23 pages, one column, final published versio
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