Information geometry, asymptotic normality and metrology for quantum input-output systems

Information geometry, asymptotic normality and metrology for quantum input-output systems

Seminar author:Madalin Guta

Event date and time:06/10/2021 04:00:pm

Event location:https://us02web.zoom.us/j/88343510649?pwd=cmVnWnpXMHBJdUJScVhOQWRydFR3Zz09

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Markov theory plays a central role in the study of open quantum systems. In this presentation I will discuss the problem of identifying and estimating dynamical parameters of quantum Markov processes, in the input-output formalism. I will consider several aspects of this problem: The first one concerns the structure of the space of identifiable parameters for ergodic dynamics, assuming full access to the output state for arbitrarily long times. The second aspect concerns the information geometric structure on this space. I will show that the space of identifiable parameters carries a Riemannian metric based on the quantum Fisher information of the output. The metric can be computed explicitly in terms of the Markov covariance of certain fluctuation operators. The third aspect concerns the asymptotic statistical structure of the output state. I will show that the output state satisfies local asymptotic normality, i.e. they can be approximated by a quantum Gaussian shift model constructed from the Markov covariance data. Finally, I will discuss a connection between dynamical phase transitions and quantum enhanced metrology with input-output systems and possible measurement strategies for optimal estimation.