Deterministic submanifolds and analytic solution of the quantum stochastic differential master equation describing a monitored qubit

Alain Sarlette 1 Pierre Rouchon 1, 2
1 QUANTIC - QUANTum Information Circuits
Inria de Paris, MINES ParisTech - École nationale supérieure des mines de Paris, UPMC - Université Pierre et Marie Curie - Paris 6, ENS Paris - École normale supérieure - Paris
Abstract : This paper studies the stochastic differential equation (SDE) associated to a two-level quantum system (qubit) subject to Hamiltonian evolution as well as unmonitored and monitored decoherence channels. The latter imply a stochastic evolution of the quantum state (density operator), whose associated probability distribution we characterize. We first show that for two sets of typical experimental settings, corresponding either to weak quantum non demolition measurements or to weak fluorescence measurements, the three Bloch coordinates of the qubit remain confined to a deterministically evolving surface or curve inside the Bloch sphere. We explicitly solve the deterministic evolution, and we provide a closed-form expression for the probability distribution on this surface or curve. Then we relate the existence in general of such deterministically evolving submanifolds to an accessibility question of control theory, which can be answered with an explicit algebraic criterion on the SDE. This allows us to show that, for a qubit, the above two sets of weak measurements are essentially the only ones featuring deterministic surfaces or curves.
Type de document :
Article dans une revue
Journal of Mathematical Physics, American Institute of Physics (AIP), 2017, 58 (6), pp.1-28. 〈10.1063/1.4984587〉
Liste complète des métadonnées

Littérature citée [15 références]  Voir  Masquer  Télécharger

https://hal-mines-paristech.archives-ouvertes.fr/hal-01635290
Contributeur : François Chaplais <>
Soumis le : mercredi 15 novembre 2017 - 03:29:38
Dernière modification le : jeudi 26 avril 2018 - 10:29:05
Document(s) archivé(s) le : vendredi 16 février 2018 - 12:46:51

Fichier

1603.05402.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Alain Sarlette, Pierre Rouchon. Deterministic submanifolds and analytic solution of the quantum stochastic differential master equation describing a monitored qubit. Journal of Mathematical Physics, American Institute of Physics (AIP), 2017, 58 (6), pp.1-28. 〈10.1063/1.4984587〉. 〈hal-01635290〉

Partager

Métriques

Consultations de la notice

294

Téléchargements de fichiers

58