Zero-error communication under discrete-time Markovian dynamics - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Zero-error communication under discrete-time Markovian dynamics

Résumé

Consider an open quantum system with (discrete-time) Markovian dynamics. Our task is to store information in the system in such a way that it can be retrieved perfectly, even after the system is left to evolve for an arbitrarily long time. We show that this is impossible for classical (resp. quantum) information precisely when the dynamics is mixing (resp. asymptotically entanglement breaking). Furthermore, we provide tight universal upper bounds on the minimum time after which any such dynamics `scrambles' the encoded information beyond the point of perfect retrieval. On the other hand, for dynamics that are not of this kind, we show that information must be encoded inside the peripheral space associated with the dynamics in order for it to be perfectly recoverable at any time in the future. This allows us to derive explicit formulas for the maximum amount of information that can be protected from noise in terms of the structure of the peripheral space of the dynamics.
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Dates et versions

hal-04844856 , version 1 (18-12-2024)

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Satvik Singh, Mizanur Rahaman, Nilanjana Datta. Zero-error communication under discrete-time Markovian dynamics. 2024. ⟨hal-04844856⟩
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