Perry, CD; (2016) Conclusive exclusion of quantum states and aspects of thermo-majorization. Doctoral thesis , UCL (University College London).

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Abstract

Part 1: Why can we not distinguish between pure, non-orthogonal quantum states? Regarding the quantum state as a state of knowledge rather than something physically real, has the potential to answer this question and explain other quantum properties but such interpretations have recently been undermined. This important no-go result, due to Pusey, Barrett and Rudolph, makes use of a specific example of a task we term state exclusion. Here, a system is prepared in a state chosen from a known set and the aim is to determine a preparation that has not taken place. We formulate state exclusion as a semidefinite program, using it to investigate when exclusion is conclusively possible and how it can be achieved. Based on state exclusion, we construct a communication task which exhibits drastic, `infinite', separations between a variety of classical and quantum information and communication complexity measures. This serves to requisition the aforementioned foundational result for use in information theoretic protocols. Part 2: What does thermodynamics look like in the absence of the thermodynamic limit? In recent years there has been a concerted effort to apply techniques from quantum information theory to study the laws of thermodynamics at the nano-scale. This has led to the resource theory of thermal operations for determining when single-copy transformations are possible. However, if a deterministic transition is forbidden, can it occur probabilistically? Here we compute and bound the maximum probability with which nano-scale thermodynamical transformations can occur. Thermal operations assume that one can precisely manipulate all of the degrees of freedom in a very large heat bath. While this enables the derivation of ultimate limits on nano-scale thermodynamics, it does not make them feasible to perform in reality. We show how allowed transitions can be implemented whilst manipulating only a single bath-qubit, making thermal operations more experimentally palatable.

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