Exact solution for the evolution of a qubit under continuous measurement

Alain Sarlette 1 Pierre Rouchon 1, 2
1 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, MINES ParisTech - École nationale supérieure des mines de Paris, CNRS - Centre National de la Recherche Scientifique : UMR8551
Abstract : We analyze an experiment with continuous heterodyne measurement of an energy loss operator on a superconducting qubit. We have observed that in the associated mathematical model, due to the degeneracy of the diffusion operator, the resulting quantum trajectories are supported not in the entire Bloch sphere, but instead they belong to the surface of a deterministically evolving ellipsoid. This allows to analytically solve for the probability distribution of the prior-to-measurement quantum state, governed by the stochastic differential master equation.
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https://hal.inria.fr/hal-01248801
Contributor : Alain Sarlette <>
Submitted on : Tuesday, December 29, 2015 - 3:26:09 PM
Last modification on : Wednesday, May 15, 2019 - 3:35:48 AM

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  • HAL Id : hal-01248801, version 1

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Alain Sarlette, Pierre Rouchon. Exact solution for the evolution of a qubit under continuous measurement. International Conference on Industrial and Applied Mathematics, Aug 2015, Beijing, China. ⟨hal-01248801⟩

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