Quantum Causality

Causality is a fundamental concept in physics; an event A causing an event B must precede it in time. All fundamental theories of physics assume a definite order of event and allow to say to say without ambiguity if A is in the causal past of B, the opposite or the two are space-like separated.

In a nutshell, Quantum Causality is a recently new research avenue in Quantum Mechanics which deconstructs this well definite causal structure. This is done for multiple reasons such as gaining insights into the quest for the unification of Quantum Theory with General Relativity into a theory of Quantum Gravity and acheiving computational advantages through causally indefinited processes.

I did my master thesis at QuIC under the supervision of Professor Ognyan Oreshkov, Julian Wechs and Ravi Kunjwal. I loved the subject because it addressed some very fascinating questions and gave me the opportunity to delve into highly fundamental physics. Here is a download link to my master thesis: Shift basis distinguishability using time-delocalized realization of the Lugano process .pdf

The main result of my thesis is the design of this lovely quantum circuit, which has some very beautiful properties.

Abstract

The process matrix formalism offers a description of quantum theory without a well-defined causal structure, which could potentially have relevance for quantum gravity. This formalism allows for the description of causally indefinite processes, with one notable example being the quantum switch, which has been experimentally realized and has demonstrated computational advantages that are unreachable in situations with a definite causal structure.

This thesis focuses on another causally indefinite process, known as the Lugano process, which has been proven to achieve something impossible by quantum nonlocality without entanglement (QNWE) in a situation with a well-defined causal order: the establishment of a protocol using only local operations and classical communication (LOCC) that implements a complete measurement of a set of unentangled orthogonal states called the Shift basis.

The main objective of this master’s thesis is to investigate the implementation of this protocol in a temporally ordered circuit established using a time-delocalized description of the Lugano process, known as the Lugano circuit. The central research question focuses on understanding how the ability of the Lugano process to achieve the LOCC Shift basis measurement protocol manifests itself in the Lugano circuit.

Unitaries inspired by the protocol are devised and incorporated into the Lugano circuit, resulting in a circuit which exhibits interesting properties that enable a complete measurement of the Shift basis. A LOCC protocol is established using this result, allowing for the distinction of the first six Shift states and the detection of the presence of the last two without distinguishing between them.

To gain further insights, the Lugano circuit is converted into an acausal circuit using time-delocalized subsystems, where the conceived unitaries are inserted. This computation aims to identify the fundamental step that corresponds to the trade-off between complete distinguishability under LOCC and indefinite causal order.

Overall, this thesis contributes to the understanding of the relationship between indefinite causal structure and QNWE. A notable further investigation suggested is to pursue the computation into the acausal circuit and analyze its capabilities.