Supervision : Elham KASHEFI

Co-supervision : MANSFIELD Shane

The interplay between quantum contextuality and Wigner negativity

Quantum physics has revolutionised our way of conceiving nature and is now bringing about a new technological revolution. The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance.
This thesis focuses on two nonclassical behaviours: quantum contextuality and Wigner negativity. The former is a notion superseding non-locality that can be exhibited by quantum systems. To date, it has mostly been studied in discrete-variable scenarios, where observables take values in discrete and usually finite sets. In those scenarios, contextuality has been shown to be necessary and sufficient for advantages in some cases. On the other hand, negativity of the Wigner function is another unsettling non-classical feature of quantum states that originates from phase-space formulation in continuous-variable quantum optics. Continuous-variable scenarios offer promising candidates for implementing quantum computations and informatics protocols. Wigner negativity is known to be a necessary resource for quantum speedup with continuous variables. However contextuality has been little understood and studied in continuous-variable scenarios.
We first set out a robust framework for properly treating contextuality in continuous variables. We also quantify contextuality in such scenarios by using tools from infinite-dimensional optimisation theory. This is achieved by a converging hierarchy of finite-dimensional semidefinite programs that approximates the contextual fraction.
Building upon this, we show that Wigner negativity is equivalent to contextuality in continuous variables with respect to Pauli measurements thus establishing a continuous-variable analog of a celebrated result by Howard et al. in discrete variables.
We then introduce experimentally friendly witnesses for Wigner negativity of single mode and multimode quantum states, based on fidelity with Fock states. They possess a threshold expectation value indicating whether the measured state has a negative Wigner function. We phrase the problem of finding the threshold values as infinite-dimensional linear programs, and we derive two converging hierarchies of semidefinite programs to approximate the threshold values.
We further extend the range of previously known discrete-variable results linking contextuality and advantage into a new territory of information retrieval. We introduce a discrete-variable communication game - called the Torpedo Game - where perfect quantum strategies stem from negativity of the discrete Wigner function. Sequential contextuality is shown not only to be necessary and sufficient for quantum advantage, but also to quantify the degree of advantage for information retrieval tasks.

2021-2024 Publications

• 2024
  • G. De Gliniasty, P. Hilaire, P.‑E. Emériau, Stephen C. Wein, A. Salavrakos, Sh. Mansfield : “A Spin-Optical Quantum Computing Architecture”, (2024)
• 2023
  • K. Vallée, P.‑E. Emériau, B. Bourdoncle, A. Sohbi, Sh. Mansfield, D. Markham : “Corrected Bell and Noncontextuality Inequalities for Realistic Experiments”, (2023)
• 2022
  • R. Booth, U. Chabaud, P.‑E. Emériau : “Contextuality and Wigner negativity are equivalent for continuous-variable quantum measurements”, Physical Review Letters, vol. 129 (23), pp. 230401, (American Physical Society) (2022)
  • R. Barbosa, T. Douce, P.‑E. Emériau, E. Kashefi, Sh. Mansfield : “Continuous-variable nonlocality and contextuality”, Communications in Mathematical Physics, vol. 391, pp. 1047-1089, (Springer Verlag) (2022)
  • P.‑E. Emériau, M. Howard, Sh. Mansfield : “Quantum Advantage in Information Retrieval”, PRX Quantum, vol. 3 (2), pp. 020307, (APS Physics) (2022)
• 2021
  • P.‑E. Emériau : “The interplay between quantum contextuality and Wigner negativity”, thesis, phd defence 11/02/2021, supervision Kashefi, Elham, co-supervision : Mansfield, Shane (2021)
  • U. Chabaud, P.‑E. Emériau, F. Grosshans : “Witnessing Wigner Negativity”, Quantum, vol. 5, pp. 471, (Verein) (2021)