183 research outputs found
Asymptotic expansions of Laplace integrals for quantum state tomography
Bayesian estimation of a mixed quantum state can be approximated via maximum
likelihood (MaxLike) estimation when the likelihood function is sharp around
its maximum. Such approximations rely on asymptotic expansions of
multi-dimensional Laplace integrals. When this maximum is on the boundary of
the integration domain, as it is the case when the MaxLike quantum state is not
full rank, such expansions are not standard. We provide here such expansions,
even when this maximum does not belong to the smooth part of the boundary, as
it is the case when the rank deficiency exceeds two. These expansions provide,
aside the MaxLike estimate of the quantum state, confidence intervals for any
observable. They confirm the formula proposed and used without precise
mathematical justifications by the authors in an article recently published in
Physical Review A.Comment: 17 pages, submitte
Parameter estimation from measurements along quantum trajectories
The dynamics of many open quantum systems are described by stochastic master
equations. In the discrete-time case, we recall the structure of the derived
quantum filter governing the evolution of the density operator conditioned to
the measurement outcomes. We then describe the structure of the corresponding
particle quantum filters for estimating constant parameter and we prove their
stability. In the continuous-time (diffusive) case, we propose a new
formulation of these particle quantum filters. The interest of this new
formulation is first to prove stability, and also to provide an efficient
algorithm preserving, for any discretization step-size, positivity of the
quantum states and parameter classical probabilities. This algorithm is tested
on experimental data to estimate the detection efficiency for a superconducting
qubit whose fluorescence field is measured using a heterodyne detector.Comment: 8 pages, 3 figures, submitte
Quantum state tomography with non-instantaneous measurements, imperfections and decoherence
Tomography of a quantum state is usually based on positive operator-valued
measure (POVM) and on their experimental statistics. Among the available
reconstructions, the maximum-likelihood (MaxLike) technique is an efficient
one. We propose an extension of this technique when the measurement process
cannot be simply described by an instantaneous POVM. Instead, the tomography
relies on a set of quantum trajectories and their measurement records. This
model includes the fact that, in practice, each measurement could be corrupted
by imperfections and decoherence, and could also be associated with the record
of continuous-time signals over a finite amount of time. The goal is then to
retrieve the quantum state that was present at the start of this measurement
process. The proposed extension relies on an explicit expression of the
likelihood function via the effective matrices appearing in quantum smoothing
and solutions of the adjoint quantum filter. It allows to retrieve the initial
quantum state as in standard MaxLike tomography, but where the traditional POVM
operators are replaced by more general ones that depend on the measurement
record of each trajectory. It also provides, aside the MaxLike estimate of the
quantum state, confidence intervals for any observable. Such confidence
intervals are derived, as the MaxLike estimate, from an asymptotic expansion of
multi-dimensional Laplace integrals appearing in Bayesian Mean estimation. A
validation is performed on two sets of experimental data: photon(s) trapped in
a microwave cavity subject to quantum non-demolition measurements relying on
Rydberg atoms; heterodyne fluorescence measurements of a superconducting qubit.Comment: 11 pages, 4 figures, submitte
Dimitri FILIMONOV, Raconter la France aux Soviétiques. Une histoire du journalisme international en URSS entre 1946 et 1958
Issu dâune thĂšse de doctorat en Ă©tudes slaves soutenue en 2019 Ă lâuniversitĂ© Paris 8, lâouvrage de Dimitri Filimonov propose une histoire du journalisme international en URSS entre 1946 et 1958. Ce travail sâinscrit principalement dans deux courants distincts de lâhistoriographie. Un premier dĂ©diĂ© au journalisme a cherchĂ© Ă saisir la presse moins comme une source que comme un objet dâĂ©tude Ă part entiĂšre dans une analyse du pouvoir en URSS. En France, les travaux prĂ©curseurs de Gabor Ritter..
French Roadmap for complex Systems 2008-2009
This second issue of the French Complex Systems Roadmap is the outcome of the
Entretiens de Cargese 2008, an interdisciplinary brainstorming session
organized over one week in 2008, jointly by RNSC, ISC-PIF and IXXI. It
capitalizes on the first roadmap and gathers contributions of more than 70
scientists from major French institutions. The aim of this roadmap is to foster
the coordination of the complex systems community on focused topics and
questions, as well as to present contributions and challenges in the complex
systems sciences and complexity science to the public, political and industrial
spheres
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