A pedagogical introduction to continuously monitored quantum systems and measurement-based feedback

• URL: http://arxiv.org/abs/2312.13214v1
• Date: Wed, 20 Dec 2023 17:31:19 GMT
• Title: A pedagogical introduction to continuously monitored quantum systems and measurement-based feedback
• Authors: Francesco Albarelli and Marco G. Genoni
• Abstract summary: We start by giving a simplified derivation of the Markovian master equation in Lindblad form. The same formalism is then exploited to derive master equations that describe conditional dynamics. We focus on the two most paradigmatic examples of continuous monitoring.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this manuscript we present a pedagogical introduction to continuously monitored quantum systems. We start by giving a simplified derivation of the Markovian master equation in Lindblad form, in the spirit of collision models and input-output theory, which describes the unconditional dynamics of a continuously monitored system. The same formalism is then exploited to derive stochastic master equations that describe the conditional dynamics. We focus on the two most paradigmatic examples of continuous monitoring: continuous photodetection, leading to a discontinuous dynamics with "quantum jumps", and continuous homodyne measurements, leading to a diffusive dynamics. We then present a derivation of feedback master equations that describe the dynamics (either conditional or unconditional) when the continuous measurement photocurrents are fed back to the system as a linear driving Hamiltonian, a paradigm known as linear Markovian feedback. In the second part of the manuscript we focus on continuous-variable Gaussian systems: we first present the equations for first and second moments describing the dynamics under continuous general-dyne measurements, and we then discuss in more detail the conditional and unconditional dynamics under Markovian and state-based feedback.

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