Madalin Guta

System Identification for Passive Linear Quantum Systems

System identification is a key enabling component for the implementation of quantum technologies, including quantum control. In this paper, we consider the class of passive linear input-output systems, and investigate several basic questions: 1) which parameters can be identified? 2) Given sufficient input-output data, how do we reconstruct the system parameters? 3) How can we optimize the estimation precision by preparing appropriate input states and performing measurements on the output? We show that minimal systems can be identified up to a unitary transformation on the modes, and systems satisfying a Hamiltonian connectivity condition called “infecting” are completely identifiable. We propose a frequency domain design based on a Fisher information criterion, for optimizing the estimation precision for coherent input state. As a consequence of the unitarity of the transfer function, we show that the Heisenberg limit with respect to the input energy can be achieved using non-classical input states.

Equivalence Classes and Local Asymptotic Normality in System Identification for Quantum Markov Chains

We consider the problem of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. The starting point of the analysis is the fact that the knowledge of the output state completely fixes the dynamics up to an equivalence class of ‘coordinate transformation’ consisting of a multiplication by a phase and a unitary conjugation of the Kraus operators.Assuming that the dynamics depends on an unknown parameter, we show that the latter can be estimated at the ‘standard’ rate n−1/2, and give an explicit expression of the (asymptotic) quantum Fisher information of the output, which is proportional to the Markov variance of a certain ‘generator’. More generally, we show that the output is locally asymptotically normal, i.e., it can be approximated by a simple quantum Gaussian model consisting of a coherent state whose mean is related to the unknown parameter. As a consistency check, we prove that a parameter related to the ‘coordinate transformation’ unitaries has zero quantum Fisher information.

Beating the Standard Quantum Limit in Quantum Metrology despite Noise

We review the quantum information theory program analysing the impact of noise in quantum metrology, which has led to the first uncorrelated-noise model allowing for limitless quantum enhancement of measurement precision, consequently yielding an improved atomic magnetometry experimental proposal.