Information theoretic resources in quantum theory

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 to account for both fundamental restrictions on operations, such as those arising from superselection rules, as well as experimental errors arising from the imperfections in the apparatus. 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. Following the treatment of effective entanglement, we focus on a related concept of nonlocality in the presence of superselection rules (SSR). Here we propose a scheme that may be used to activate nongenuinely multipartite nonlocality, in that a single copy of a state is not multipartite nonlocal, while two or more copies exhibit nongenuinely multipartite nonlocality. The states used exhibit the more powerful genuinely multipartite nonlocality when SSR are not enforced, but not when they are, raising the question of what is needed for genuinely multipartite nonlocality. We show that whenever the number of particles is insufficient, the degrading of genuinely multipartite to nongenuinely multipartite nonlocality is necessary. While in the first few chapters we focus our attention 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 - we show it can be interpreted as the difference in superdense coding capacity between a quantum state and a classical state.EThOS - Electronic Theses Online ServiceGBUnited Kingdo