Indefinite causal orders in thermodynamics and from time superpositions

Thesis

This thesis is concerned with the use of indefinite causal orders (ICOs) for thermodynamic tasks, and a new context in which these exotic causal structures might arise — from superpositions in time. I propose a thermodynamic refrigeration cycle which uses indefinite causal orders to achieve non-classical cooling. The cycle cools a cold reservoir while consuming purity in a control qubit. I first show that the application to an input state of two identical thermalising channels of temperature T in an indefinite causal order can result in an output state with a temperature not equal to T. This result allows the construction of the refrigeration cycle. I investigate its properties and show that thermodynamically, the result is compatible with unitary quantum mechanics in the circuit model, but could not be achieved classically. This result suggests the development of a new class of thermodynamic resource theories in which operations are allowed to be performed in an indefinite causal order. I proceed to detail a simulation of the protocol using the IBM cloud quantum computing service, which is open to all users of the internet. The simulation, which is itself a quantum refrigerator, shows that the refrigeration cycle is robust to noise and can be implemented on Noisy Intermediate-Scale Quantum (NISQ) devices. This represents the development of a promising new test-bed for ICO protocols. Finally, the possibility for ICOs to arise from superpositions in time is considered. A new formalism, developed to analyse such superpositions, is applied to the case of two events which have a quantum uncertainty associated with their times. It is shown that these events can be used as triggers which enable an ICO. The fact that such commonplace phenomena can give rise to indefinite causal orders suggests that they might be much more common in nature than is typically understood.

Authors: Felce, D

• DOI: 10.5287/ora-7rj00oapb
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: quantum refrigeration; indefinite causal orders; quantum thermodynamics; superpositions in time
• Subjects: Causality (Physics); Quantum computing; Thermodynamics; Quantum theory