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Capacities of quantum Markovian noise for large times
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Given a quantum Markovian noise model, we study the maximum dimension of a classical or quantum system that can be stored for arbitrarily large time. We show that, unlike the fixed time setting, in the limit of infinite time, the classical and quantum capacities are characterized by efficiently computable properties of the peripheral spectrum of the quantum channel. In addition, the capacities are additive under tensor product, which implies in the language of Shannon theory that the one-shot and the asymptotic i.i.d. capacities are the same. We also provide an improved algorithm for computing the structure of the peripheral subspace of a quantum channel, which might be of independent interest.
Forward citations
Cited by 2 Pith papers
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Fixed points in de Finetti hierarchies
Fixed-point constraints on de Finetti hierarchies yield O(√(log n)/n) double-sided rates, block-structured dimension dependence, and poly-time certifiable separable inner approximations for fixed local dimensions.
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Sequential transmission at short times
The paper proves that if each coded channel is epsilon-close to the identity in diamond norm, the n-fold sequential composition has one-shot quantum capacity at least 1 - 2n epsilon minus a small entropy term.
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