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Title: Quantum correlations in space-time : foundations and applications
Author: Zhang, Tian
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2020
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The absolute/relative debate on the nature of space and time is ongoing for thousands of years. Here we attempt to investigate space and time from the information theoretic point of view to understand spatial and temporal correlations under the relative assumption. Correlations, as a measure of relationship between two quantities, do not distinguish space and time in classical probability theory; quantum correlations in space are well-studied but temporal correlations are not well understood. The thesis investigates quantum correlations in space-time, by treating temporal correlations equally in form as spatial correlations and unifying quantum correlations in space and time. In particular, we follow the pseudo-density matrix formalism in which quantum states in spacetime are properly defined by correlations from measurements. We first review classical correlations, quantum correlations in space and time, to motivate the pseudo-density matrix formalism in finite dimensions. Next we generalise the pseudo-density matrix formulation to continuous variables and general measurements. Specifically, we define Gaussian spacetime states by the first two statistical moments, and for general continuous variables spacetime states are defined via the Wigner function representation. We also define spacetime quantum states in position measurements and weak measurements for general measurement processes. Then we compare the pseudo-density matrix formalism with other spacetime formulations: indefinite causal structures, consistent histories, generalised non-local games, out-of-time-order correlation functions, and path integrals. We argue that in non-relativistic quantum mechanics, different spacetime formulations are closely related and almost equivalent via quantum correlations, except path integrals. Finally, we apply the pseudo-density matrix formulation to time crystals. By defining time crystals as long-range order in time, we analyse continuous and discrete time translation symmetry as well as discuss the existence of time crystals from an algebraic point of view. Finally, we summarise our work and provide the outlook for future directions.
Supervisor: Vedral, Vlatko Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: quantum information