Hi all,
Tomorrow we will have two talks. Eliot Jean will tell us about his master thesis with Vilasini and Ralph Silva, entitled 'Connecting the Multi-Time Formalism and Post-Selected Closed Timelike Curves' and Matthias Salzger will tell us about his master thesis with Vilasini entitled 'Connecting indefinite causal order processes to composable quantum protocols in a spacetime'. See below for the abstracts. The talks will take place at 2pm in F31.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best, Ladina
%%%%%
Title: Connecting the Multi-Time Formalism and Post-Selected Closed Timelike Curves
Abstract: In this work, two different models are reviewed and relations between the two are derived. On the one hand, the multi-time formalism is a time-symmetric formulation of quantum mechanics. It allows to describe experiments with multiple preparation and measurement stages and, in particular, pre- and post-selected systems. On the other hand, the model of post-selected closed timelike curves (P-CTCs) is a particular quantum model for CTCs, which formalizes physically the notion of time travel. It was already shown that linear two-time states and linear P-CTCs are related to process matrices. This suggested that linear two-time states and linear P-CTCs are actually equivalent. What about the spaces of general two-time states, or even multi-time states, and general P-CTCs? It is shown that any pure two-time operator can be implemented up to proportionality using a circuit assisted by a single P-CTC. Furthermore, multi-time states and two-time operators can be related using a circuit involving at most the same number of P-CTCs as there are backward-evolving states in the related multi-time state. Finally, mixed two-time operators can be achieved using a mixture of P-CTC-assisted circuits.
Title: Connecting indefinite causal order processes to composable quantum protocols in a spacetime
Abstract: Process matrices provide a general framework to model quantum information processing protocols without assuming a fixed and acyclic background spacetime. However, it is an open question to characterize the subset of processes that are physically realizable in a fixed background spacetime. A related question is that process matrices are known to be non-composable while composability is a basic property of physical processes. A bottom-up approach to characterizing physical processes is given by the framework of quantum circuits with quantum control of causal order (QC-QC). On the other hand, a recent top-down approach to the problem connects to the framework of causal boxes, which models composable physical protocols in a background spacetime, while allowing for quantum states to be delocalized in space and in time. The subset of causal boxes that incorporate the set-up assumptions of the process framework correspond to so-called process boxes. Here we address the physicality and composability questions for process matrices by connecting these bottom-up and top-down approaches. We first give a procedure for modelling each QC-QC as a causal box. This allows us to define composition of QC-QCs in terms of composition of causal boxes and resolves the composability problem. We then consider the mapping from process boxes to QC-QCs. Our results suggest that the general class of processes that can be physically implemented in a fixed background spacetime are those that can be interpreted as QC-QCs. Intuitively, this result follows from the physical principle of relativistic causality in the background spacetime. This provides an avenue for exploring further connections between information-theoretic and spacetime related causality notions, and composability of physical experiments.