Causality in quantum information – CausaQ
Non-Local Games help characterize the nature and power of quantum correlations, via multi-party tasks which can only be achieved thanks to the use of quantum physics. They allow a combinatorial approach to these issues. Quantum Cellular Automata are the mathematical framework in which to model discrete spacetime quantum phenomena. Their understanding is key to quantum simulation (i.e. the use of a quantum system in order to emulate another) and for theoretical physics. The tools there are those of linear algebra and numerical analysis. Quantum Secret Sharing (QSS) aims at hiding a classical or quantum secret by encoding it within a quantum state, which is then shared amongst the different parties. The secret can only be retrieved if a certain proportion of the parties cooperate. This themes uses techniques from graphs and rewriting. In each of the three themes, the spatial organisation of quantum data, and the way this limits their access, are the key factor : these are three aspects of the causality of quantum information.
The Church-Turing thesis states that « Anything which can be computed, can be computed with a Turing machine. ». It is the socle upon which modern Computer Science is built. Gandy, a student of Turing, has made this thesis into a theorem –- which follows from simple assumptions about physics (homogeneity, locality, finiteness of the density of information). We extended this theorem to account for quantum physics.
Popular science :
- La Chronique Info-Sciences de France Info.
- Simon Martiel, co-supervised PhD student, won the JTF Turing Scholar prize.
- 2 papers in « La Recherche », 1 in « Physics World ».
This research has opened new perspectives for instance in:
* Cryptography: Quantum Secret Sharing
* Computability: Church-Turing thesis in a quantum setting
* Quantum simulation: of fundamental particles, noisy simulation
* Models of computation: Causal Graph Dynamics...
This ANR project has led to 11 publications in international, peer-reviewed journals, and 21 publications in peer-reviewed international conferences.
In near future, Information Technology will have to confront the challenges of the fundamentally quantum nature of physical embodiments of computing systems. This passage to quantum information technology is both a matter of necessity and one which offers many new opportunities.
From a scientific point of view however the countours of this quantum information processing revolution are not well-understood. Most researchers feel we have not yet grasped the fundamental strengths and limits to quantum information processing. In other words we do not have, yet, a theory which would help us understand why some tasks can be improved by going quantum, and why some other tasks cannot be improved. Such an agenda has been pursued in the past via the study of entanglement as the fundamental resource. It has yielded many results, some of them convoluted, and recently infanted a new simpler and promising route: that of the study of causality.
Taking the view of causality has given unexpected progress in several directions. For instance in quantum information it has been shown that main quantum cryptographic protocols can be obtained from the abstract notion of nonlocality alone.
In this proposal we make a concerted, coherent approach to see how best we can understand causality in the context of quantum information processing. We consider three ways to characterize causality in quantum information processing:
• By transfomations, using the measurement based model to analyse the information : flow on
graph states
• By tasks, precisely we consider non local-boxes and try to give a combinatorial characterization of causality for games.
• By axiomatics, considering quantum cellular automata and the effects of causality when
we restrict only close cells to share randomness.
Hence concerte approach of a same concept by different interconnected methods and models. We begin with quantum information, via the study of simple multi-party protocols (aka games) which characterize and take advantage of causality, thereby hoping to induce new cryptographic schemes / understanding of the previous one. We seek to establish a formal connection with the notion of “flow” in measurement-based quantum computing, which clearly exhibits a causality structure and is known to have applications in terms of multi-party cryptography and secure computation and rewriting programs. This notion of “flow” arises as a condition for computability in measurement-based quantum computation, and so this takes us to investigate a fundamental connection between causal operators and their ability to compute, especially in open systems.
Our focus is always on understanding the strength and limits of quantum information processing with causality as the guiding line, i.e. seeking to identify and extend the cases where it can be useful, and hence draw sharper its contours, at a scientific level.
Project coordination
Pablo ARRIGHI (UNIVERSITE GRENOBLE I [Joseph Fourier]) – pablo.arrighi@imag.fr
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
Partner
LIG UNIVERSITE GRENOBLE I [Joseph Fourier]
Help of the ANR 277,040 euros
Beginning and duration of the scientific project:
- 48 Months
