Emergence of jumps in quantum trajectories via homogeneization

Abstract

In the strong noise regime, we study the homogeneization of quantum trajectories i.e. stochastic processes appearing in the context of quantum measurement. When the generator of the average semi-group can be separated into three distinct time scales, we start by describing a homogenized limiting semi-group. This result is of independent interest and is formulated outside of the scope of quantum trajectories. Going back to the quantum context, we show that, in the Meyer-Zheng topology, the time-continuous quantum trajectories converge weakly to the discontinuous trajectories of a pure jump Markov process. Notably, this convergence cannot hold in the usual Skorokhod topology.

48 pages, no figures. v1: Preliminary version. v2: Minor changes in presentation, submitted version

References in corpus (7)

• Progressive field-state collapse and quantum non-demolition photon counting
• Universal oscillations in counting statistics
• A discrete invitation to quantum filtering and feedback control
• Existence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case
• Uniqueness of thermodynamic projector and kinetic basis of molecular individualism
• Adiabatic elimination in quantum stochastic models
• Computing the Rates of Measurement-Induced Quantum Jumps

Cited by in corpus (5)

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