Zero-error communication under discrete-time Markovian dynamics

Abstract

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.

Close to the published version

References in corpus (25)

• Quantum Computing in the NISQ era and beyond
• Quantum collision models: open system dynamics from repeated interactions
• Quantum f-divergences and error correction
• Improving zero-error classical communication with entanglement
• Zero-error communication via quantum channels, non-commutative graphs and a quantum Lovasz theta function
• A quantum version of Wielandt's inequality
• Ergodic and Mixing Quantum Channels in Finite Dimensions
• Sufficiency in quantum statistical inference
• Zero-error channel capacity and simulation assisted by non-local correlations
• No-Signalling Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number
• Open dynamics under rapid repeated interaction
• Complementarity of Private and Correctable Subsystems in Quantum Cryptography and Error Correction
• Entanglement can increase asymptotic rates of zero-error classical communication over classical channels
• Diagonal unitary and orthogonal symmetries in quantum theory
• On superactivation of zero-error capacities and reversibility of a quantum channel
• The multiplicative domain in quantum error correction
• Families of completely positive maps associated with monotone metrics
• Contraction coefficients for noisy quantum channels
• Multiplicative Properties of Quantum Channels
• Entanglement-Saving Channels
• Eventually entanglement breaking Markovian dynamics: structure and characteristic times
• Spectral Properties of Tensor Products of Channels
• Ergodic theory of diagonal orthogonal covariant quantum channels
• A generic quantum Wielandt's inequality
• Quantum relative entropy: general convergence criterion and preservation of convergence under completely positive linear maps