Quantum Markov semigroups on d-dimensional systems have infinite-time capacities determined by peripheral space structure, with convergence after time t ≳ d² ln(d), and explicit bounds showing n-qubit memories fail after t ≳ n 2^{2n} (global correction) or t ≳ ln(n) (local).
Quantum Channels, Wavelets, Dilations and Representations of $O_n$
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abstract
We show that the representations of the Cuntz C$^\ast$-algebras $O_n$ which arise in wavelet analysis and dilation theory can be classified through a simple analysis of completely positive maps on finite-dimensional space. Based on this analysis, an application in quantum information theory is obtained; namely, a structure theorem for the fixed point set of a unital quantum channel. We also include some open problems motivated by this work.
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quant-ph 1years
2025 1verdicts
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Information storage and transmission under Markovian noise
Quantum Markov semigroups on d-dimensional systems have infinite-time capacities determined by peripheral space structure, with convergence after time t ≳ d² ln(d), and explicit bounds showing n-qubit memories fail after t ≳ n 2^{2n} (global correction) or t ≳ ln(n) (local).