Quantum Shannon theory in the presence of indefinite causal order

Lead Research Organisation: University of Oxford
Department Name: Computer Science

Abstract

This project falls within the EPSRC Quantum Technologies research theme, or more specifically under the Quantum Optics and Information research area.

Traditionally, information transfer in quantum information (Shannon) theory has been studied in the context of quantum communication channels operating in a definite causal order. Such definite ordering of causes and effects is implicitly assumed in classical physics. However, the relaxation of this assumption has been shown to be consistent with quantum physics, and recent research has moreover suggested that it can facilitate significant advantages in quantum communication The aim of the project is to investigate the effects of using quantum channels set up in an indefinite causal order within quantum Shannon theory and their potential applications. The project is inspired by the result, showing that two identical completely depolarising channels, which normally cannot transfer information, can be combined in a quantum superposition of alternative causal orders in a way that does allow information transfer. The novel idea enables quantum channels, which can process superpositions of quantum mechanical inputs and outputs, to also be combined in a quantum superposition themselves. Such information transfer where none would normally be possible opens up the possibility of a new paradigm in quantum communication, where communication channels are operated in various superpositions of causal orders.

In order to fully understand the advantages of this new paradigm, the capacities associated with information transfer across channels combined in an indefinite causal order must be calculated and compared with those found under definite causal order. This will be the starting point of the project. These investigations require the development of new techniques, combining standard methods of quantum Shannon theory with more recent frameworks introduced to describe indefinite causal structures. In particular, these include theframeworks of higher order maps, as well as process matrices, developed in Categorical quantum mechanics could also be used, where a recent paper has
incorporated indefinite causal order into a framework for describing quantum causal structures.

Once a framework has been established for describing channels with indefinite causal order and the potential advantages they provide quantified, the project may take one of several directions. One possibility is to investigate specific quantum communication tasks which could take advantage of indefinite causal orderings. Another interesting direction would be o consider the implications of indefinite causal structures for the foundations of quantum
mechanics. Following the informational axiomatic approach, the causality axiom and its consequences could be revisited with the explicit possibility of indefinite causal order. This could be combined with investigations into what sort of indefinite causal structures might already exists in nature, and in what sort of physical regimes they could manifest themselves. Such foundational research may have important implications in the
construction of a theory of quantum gravity, as it combines a non-fixed causal structure from general relativity with probabilistic features of quantum mechanics.

This is a theoretical project; nevertheless, experimental implementations of the results are important when going forward in realising the practical potential of indefinite causal structures. The first step to experimentally create a process without definite causal order was achieved just last year. This project is expected to involve collaboration with Philip Walter's research group at the University of Vienna, which is currently implementing the proposal, of quantum communication with depolarising channels arranged in an indefinite causal order. Other potential collaborators include Masahito Hayashi at Nagoya University and Yuxiang Yang at at ETH Zurich

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R513295/1 01/10/2018 30/09/2023
2053094 Studentship EP/R513295/1 01/10/2018 30/09/2022 Hler Kristjansson