Quantum Foundations in the light of Quantum Information – QIFound

The methods we will used are mainly inspired by new tools developed in the fields of quantum information and quantum foundations. In particular:

- for the uncertainty relations, we will use entropic measures from quantum information to quantify the amount of information gained or lost (due to disturbance) in a quantum measurement;

- for the study of non locality in quantum networks, we will base our work on the concept of «bilocality« (or «N-locality«, more generally) of correlations, which we recently introduced, and also on the well-developed study of causal models;

- to study the status of the wave function, we will use the framework of ontological models formalised recently;

- to study quantum causal relations, we will resort to the recently developed formalism of process matrices.

- Uncertainty relations :
We have derived new tight, state-independent uncertainty relations for qubits, which can be written both in terms of standard deviations or entropies [A. Abbott et al., arXiv:1512.02383].

- Quantum nonlocality:
In collaboration with the group of Nicolas Gisin in Geneva (Switzerland), we showed how to construct in a recursive manner new Bell inequalities to characterise nonlocality in quantum networks; our results have been published [D. Rosset et al, PRL 2016]

- Status of the wave function:
I showed how to elaborate a new experimental test to clarify the status of the wave function and show the limits of the epistemic view (that the wave function represents a state of knowledge) [C. Branciard, PRL 2014].
This test could be carried out experimentally in collaboration with the group of Andrew White at the University of Queensland (Australia). Our results were published in [M. Ringbauer et al., Nat. Phys. 2015].

- Quantum causality:
In collaboration with the Universities of Vienna (Austria) et of Queensland (Australia), we developed the concept of «witnesses for causal nonseparability«, in order to demonstrate teh incompatibility of certain quantum processes with any well-defined causal order [M. Araújo et al., NJP 2015]. We also showed how to characterise geometrically the set of «causal correlations«, which are compatible with a well-defined causal order, and thus derive new «causal inequalities« [C. Branciard, NJP 2016].

- Continue to derive new uncertainty relations for joint measurements, and suggest experimental tests;
explore the uncertainty principle in generalised probabilistic theories.

- Generalise the study of nonlocal correlations in quantum networks.

- Improve the tests on the status of the wave function.

- Explore further the possibility to have new types of causal relations in quantum theory (e.g. superpositions of causal orders).

- C. Branciard,
«How psi-Epistemic Models Fail at Explaining the Indistinguishability of Quantum States«,
Physical Review Letters 113, 020409 (2014).

- M. Ringbauer, B. Duffus, C. Branciard, E. G. Cavalcanti, A. G. White, and A. Fedrizzi,
«Measurements on the reality of the wave function«,
Nature Physics 11, 249 (2015).

- M. Araújo, C. Branciard, F. Costa, A. Feix, C. Giarmatzi, and C. Brukner,
«Witnessing causal nonseparability«,
New Journal of Physics 17, 102001 (2015) (Fast Track Communication).

- C. Branciard, M. Araújo, A. Feix, F. Costa, and C. Brukner,
«The simplest causal inequalities and their violation«,
New Journal of Physics 18, 013008 (2016).

- D. Rosset, C. Branciard, T. J. Barnea, G. Pütz, N. Brunner, and N. Gisin,
«Nonlinear Bell inequalities tailored for quantum networks«,
Physical Review Letters 116, 010403 (2016).

- A. A. Abbott, P.-L. Alzieu, M. J. W. Hall, and C. Branciard,
«Tight state-independent uncertainty relations for qubits«,
arXiv:1512.02383 (quant-ph).

Quantum theory is certainly one of the most successful theories, and has so far never been contradicted by any experiment. However, a clear understanding of its foundations is still missing; the intriguing question of why the world follows such puzzling rules as those of quantum theory is, after a hundred years, still begging for an answer.

Recent progress on quantum foundations has nevertheless been made possible by the emergence of quantum information. By revolutionizing the way we perceive and manipulate information, this young and very dynamic field of research has already led to a vast number of significant results, and to the development of important applications and technological advances, with a great impact on society. Quantum information has also brought major insights on quantum foundations, and has a great potential to lead to even more discoveries.

This project makes the most of these prospects. Specifically, we will revisit one of the fundamental concepts of quantum theory, namely the celebrated Heisenberg uncertainty principle, with an innovative approach and new techniques developed in the field of quantum information. One implication of the uncertainty principle is the concept of complementarity, which says that some properties of a quantum system—like for instance the location and speed of a particle—are incompatible and cannot be measured at the same time. It is however still possible to approximate a joint measurement of both properties, and gain some partial information on each of them. We will quantify precisely the optimal trade-off between the information one can obtain on each incompatible property. Although this is a very natural way of presenting the uncertainty principle and the concept of complementarity, such trade-offs have yet never been properly analysed.

Determining the amount of information obtainable through a measurement will allow us to reconsider the very limits imposed by quantum theory, and will shed a new light on its foundations. To gain more insights, we will question how much of quantum theory can be reconstructed from the concept of complementarity, taken as a fundamental axiom, and which other axioms are necessary to fully reconstruct the theory. This will give clues on why Nature chose quantum theory among other possible theories, and will offer an original perspective to the quest of the Holy Grail of quantum foundations, namely the derivation of quantum theory from more physical axioms than its standard ad hoc ones.

In addition to this specific research programme, our objective is also to launch a new research activity and establish quantum foundations as a full-fledged research domain at the Institut Néel. The Institute hosts a number of world-class experimental groups already conducting experiments in quantum information, whose know-how could directly benefit quantum foundations. This project aims at establishing a think tank to stimulate new ideas and create a fruitful synergy between our expertise in quantum foundations and the experimental capabilities already present at the Institut Néel. This will lead to the realisation of exciting and significant thought experiments testing the foundations of quantum theory, questioning our interpretations of the theory, and challenging our best understanding of the physical world.