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).
Brown, Daniel Loss, Jiannis K
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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).