Conditional and unconditional Gaussian quantum dynamics

Marco G. Genoni, Ludovico Lami, Alessio Serafini

    Research output: Contribution to journalArticleResearchpeer-review

    24 Citations (Scopus)


    © 2016 Informa UK Limited, trading as Taylor & Francis Group. This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as ‘general-dyne’) quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.
    Original languageEnglish
    Pages (from-to)331-349
    JournalContemporary Physics
    Issue number3
    Publication statusPublished - 2 Jul 2016


    • continuous monitoring
    • decoherence
    • Gaussian states
    • master equations


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