PhD student in mathematics, M/F

13 Apr 2024
Job Information

Organisation/Company

CNRS

Department

Laboratoire Paul Painlevé

Research Field

Mathematics
History » History of science

Researcher Profile

First Stage Researcher (R1)

Country

France

Application Deadline

3 May 2024 - 23:59 (UTC)

Type of Contract

Temporary

Job Status

Full-time

Hours Per Week

35

Offer Starting Date

1 Oct 2024

Is the job funded through the EU Research Framework Programme?

Not funded by an EU programme

Is the Job related to staff position within a Research Infrastructure?

No

Offer Description

The successful candidate will work in the Laboratoire Paul Painlevé, under the direction of Stephan De Bievre, in collaboration with physicists from PhLAM, specialists in particular in quantum optics, in the framework of the project "Kirkwood-Dirac and Wigner quasidistributions for Quantum Information/Communication" (KIDIWI24) financed by the MITI of the CNRS.

The idea that it should be possible to exploit the particular features of quantum systems in order to
obtain a ``quantum advantage'' has gained considerable ground in recent years and much effort has
gone into all aspects of this basic tenet, theoretically, experimentally and, more recently,
technologically. The goal is to exploit those properties that most markedly distinguish quantum systems
from classical ones to vastly improve various procedures and protocols in computing, cryptography,
communication, metrology and simulation.
A central question in this context is the identification of the classical-quantum boundary in a system's
state space. Which are the states that can or cannot be hoped to provide such a quantum advantage?
One of the tools that have proven instrumental in this questioning are quasi-probability distributions.
For the continuous variable theories, the Wigner function is central, as well as the Glauber-Sudarshan
P-function. Their negativity is a hallmark of non-classicality and a necessary condition to obtain a
possible quantum advantage. In finite dimension, Kirkwood-Dirac KD) distributions have very
recently come to the forefront in a variety of contexts. In fact, given any pair of non-commuting
observables, one can associate a KD-distribution to any quantum state. Again non-positivity is a
prerequisite here to obtain a quantum advantage.
In both cases, a number of witnesses, measures and monotones have been designed to determine if the
quasi-probability of given state does or does not manifest non-positivity and to assess the degree to
which such non-positivity is present. It is the goal of this thesis project to compare the existing such
measures through upper/lower bounds and to thus better understand their meaning and role.
No prior knowledge of quantum mechanics is required, but an interest in the application of mathematics
to physics is expected. The mathematics involved in this project is mostly functional analysis, Hilbert
space theory (operators, spectral theory) and probability theory. The capability of testing conjectures
with numerical simulations is a plus.

Requirements

Research Field

Mathematics

Education Level

Master Degree or equivalent

Research Field

History

Education Level

Master Degree or equivalent

Languages

FRENCH

Level

Basic

Research Field

Mathematics

Years of Research Experience

None

Research Field

History » History of science

Years of Research Experience

None

Additional Information

Website for additional job details

https://emploi.cnrs.fr/Offres/Doctorant/UMR8524-STEDEB-001/Default.aspx

Work Location(s)

Number of offers available

1

Company/Institute

Laboratoire Paul Painlevé

Country

France

City

VILLENEUVE D ASCQ

Geofield

Where to apply

Website

https://emploi.cnrs.fr/Candidat/Offre/UMR8524-STEDEB-001/Candidater.aspx

Contact

City

VILLENEUVE D ASCQ

Website

http://math.univ-lille1.fr/

STATUS: EXPIRED