Quantum Information in a Noisy World

Abstract

In this thesis, we investigate the problem of approximately recovering information encoded in noisy quantum systems, often focusing on the regime involving many subsystems. We study this in two very different settings: in one direction, we consider noisy quantum trees: at each node of a tree, a received qubit unitarily interacts with fresh ancilla qubits, after which each qubit is sent through a noisy channel to a different node in the next level. Therefore, as the tree depth grows, there is a competition between the irreversible effect of noise and the protection against such noise achieved by delocalization of information. We demonstrate that there is a noise threshold below which some information can be indefinitely preserved in this process, without the need for error correction. In another direction, we consider the distillation of pure states from noisy continuous variable systems (e.g., bosonic modes) using time-translation invariant (e.g., phase-insensitive) operations. We construct a novel non-Gaussian protocol to optimally distill pure coherent states from coherent thermal states in the many-copy regime. Remarkably, the lowest achievable error is determined by the inverse of the purity of coherence of the input state, a quantity obtained from the Right-Logarithmic-Derivative (RLD) Fisher information metric, hence revealing an operational interpretation of this quantity.