Information storage and transmission under Markovian noise

Satvik Singh (Technical University of Munich)

This talk is about estimating the quantum and classical capacities of quantum Markov semigroups acting on finite-dimensional quantum systems. We show that in the limit of infinite time, the capacities can be efficiently computed in terms of the structure of the peripheral space of the semigroup, are strongly additive, and satisfy the strong converse property. We also establish convergence bounds to show that the infinite-time capacities are reached after time scaling quadratically with the system dimension. From the perspective of data storage, our analysis provides tight bounds on the number of bits or qubits that can be reliably stored for long times in a quantum memory device that is experiencing Markovian noise. From the perspective of point-to-point communication between two spatially separated parties, our analysis provides efficiently computable bounds on the optimal rate at which bits or qubits can be reliably transmitted via ‘long’ Markovian communication channels, both in the finite block-length and asymptotic regimes. In order to keep the talk more accessible, I will begin with a brief introduction on the subject of quantum channel capacities.

Contact : I. Nechita