On Quantum Reading Capacities

Abstract

In this thesis, we investigate the communication scheme known as quantum reading. In this framework, classical information is encoded as a sequence of quantum channels chosen from a memory cell, and the receiver’s goal is to decode the data by solving a quantum channel discrimination problem. We explore existing versions of this scheme, deriving expressions for their capacities or, when exact formulas are unattainable, establishing lower and upper bounds. Furthermore, we introduce a novel protocol involving entanglement-assistance in the encoding, for which we provide a formula for its capacity. We then focus on specific classes of memory cells, namely jointly teleportation-simulable and jointly classical-quantum cells, where capacity computations are greatly simplified. Additionally, we numerically analyze the strict super-additivity exhibited by a memory cell consisting of two unitary channels. Finally, we establish the continuity of the quantum reading capacities and their corresponding upper bounds by employing Alicki–Fannes–Winter continuity bounds on the underlying entropic quantities