Information Theoretic Resources in Quantum Theory

TL;DR

This thesis explores the quantification and activation of quantum resources like entanglement and nonlocality under various restrictions, and introduces a measure of nonclassicality of operations relevant for quantum communication.

Contribution

It introduces new measures for effective entanglement, nonlocality activation schemes under superselection rules, and a resource-based measure of quantum operations' nonclassicality.

Findings

Linear relationship between usual and effective concurrence under errors

Activation scheme for multipartite nonlocality with multiple copies

Quantum discord interpreted as superdense coding capacity difference

Abstract

Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to perform. In the first part of this thesis we quantify the effective entanglement when operations are additionally restricted. For an important class of errors we find a linear relationship between the usual and effective higher dimensional generalization of concurrence, a measure of entanglement. In the second chapter we focus on nonlocality in the presence of superselection rules, where we propose a scheme that may be used to activate nongenuinely multipartite nonlocality with multiple copies of the state. We show that whenever the number of particles is insufficient, the genuinely multipartite nonlocality is degraded to nongenuinely multipartite. While in the first few chapters we focus on understanding the resources present in quantum states, in the final part we turn the picture around and instead treat operations themselves as a resource. We provide our observers with free access to classical operations - ie. those that cannot detect or generate quantum coherence. We show that the operation of interest can then be used to either generate or detect quantum coherence if and only if it violates a particular commutation relation. Using the relative entropy, the commutation relation provides us with a measure of nonclassicality of operations. We show that the measure is a sum of two contributions, the generating power and the distinguishing power, each of which is separately an essential ingredient in quantum communication and information processing. The measure also sheds light on the operational meaning of quantum discord, which we show can be interpreted as the difference in superdense coding capacity between a quantum state and a classical state.