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Heisenberg's uncertainty principle and the Foundations of Quantum Theory in the light of Quantum Information

Final Report Summary - QIQFOUND (Heisenberg's uncertainty principle and the Foundations of Quantum Theory in the light of Quantum Information)

Project QIQFound
Researcher: Dr Cyril Branciard (
Scientist in Charge: Dr Alexia Auffèves
Project website:

*** Summary description of the project objectives: ***

The scientific project concentrated on the Heisenberg uncertainty principle in Quantum Theory. The objectives were organized along 2 work packages. In the first work package, the objectives were to derive and investigate new uncertainty or complementarity (noise-noise or noise-disturbance) relations, with a special focus on information-theoretic perspectives (quantifying e.g. the information gained in a quantum measurement vs the information lost because of its disturbance). The second work package focused on what the uncertainty principle could teach us on quantum foundations, from a wider perspective.

Beyond the specific research program on the uncertainty principle, one stated objective of the project was, more generally speaking, to develop a new research activity on quantum foundations at the Institut Néel in Grenoble.

*** Work performed since the beginning of the project: ***

We started working on our objectives even before the project officially began; between the applications of our project and its start, we had already been able to derive new complementarity relations in terms of root-mean-square errors, and contribute to an experimental test.

During our project we could then derive new state-independent uncertainty relations for qubits (2-dimensional quantum systems), which we proved to be tight. These were expressed both in terms of standard deviations, and in terms of entropic (informational) quantities.

We also investigated the trade-off between noise and disturbance in a quantum measurement, working in an information-theoretic framework that was introduced recently. We showed that a previously derived relation was in fact not universally valid, and derived new noise-disturbance relations instead. We also derived new noise-noise relations, that quantify the trade-off between the noise on one observable vs the noise on the other, in an approximate joint measurement of two incompatible observables.

Along our second work package, we started to investigate the uncertainty principle in general probabilistic theories, to see what this could teach us on quantum foundations. This is still work in progress, which will be pursued after the end of the project.

Beyond our work on the uncertainty principle, and according to our objective of developing a new, strong research activity on quantum foundations at the Institut Néel, we worked on different other aspects of quantum foundations as well: namely, we contributed to an experimental test of the epistemic vs ontic status of the wave function in quantum theory; we investigated quantum nonlocality in quantum networks, showing how to derive Bell-like inequalities for those; we investigated which kinds of non-classical causal relations are possible in the quantum world.

All these works gave us valued opportunities to strengthen our collaborations and develop new ones with other top-level groups working in the fields of quantum foundations and quantum information worldwide.

*** Summary of the main results achieved: ***

- New state-independent uncertainty relations for qubits, both in terms of standard deviations and of entropies.

- New noise-noise and noise-disturbance relations, both in the formalism of root-mean-square errors and in the new information-theoretic framework.

- Contribution to an experimental test on the status of the wave-function.

- Development of a general method to construct Bell-like inequalities for quantum networks.

- On quantum causal relations: introduction of the concept of “causal witnesses” to check whether a quantum process is compatible with a definite causal order or not; showed how to construct new causal inequalities to test whether correlations are compatible with a definite causal order or not; extension of the latter construction to multipartite scenarios.

*** Expected final results and their potential impact and use: ***

Our investigation and derivation of new uncertainty relations brings a better understanding of the uncertainty principle in quantum theory. This opens the possibility of new experimental tests – we indeed started new collaboratiions with experimental groups for that. This will also allow for the study of possible applications in quantum information science, where uncertainty relations could be used e.g. to prove the security of certain cryptographic protocols.

Our on-going study of uncertainty relations in general probabilistic theories is also expected to provide new insights on quantum foundations, and more specifically on the relation between uncertainty and the nonlocality of quantum theory.

Our other works in quantum foundations allowed us, as planned, to develop a new research activity at the Institut Néel, which will continue beyond the present project. The project allowed us in particular to develop new long-term collaborations between the Institut Néel and other institutions in Europe and worldwide. We contributed to make the Institut Néel a major actor in the fields of quantum foundations and quantum information – two closely related fields, whose applications will have a major impact on our global information society. Our research project thereby took a role in the major international research effort on the development of quantum technologies for information processing, which will be strongly strengthened by the upcoming European Flagship on Quantum Technologies.