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CENTAUR: The system
 In Software Development Environments (SDE
, 1988
"... asymptotic normality for finite dimensional quantum ..."
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asymptotic normality for finite dimensional quantum
Asymptotic inference in system identification for the atom
, 2012
"... System identification is an integrant part of control theory and plays an increasing role in quantum engineering. In the quantum setup, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However for quantum ..."
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System identification is an integrant part of control theory and plays an increasing role in quantum engineering. In the quantum setup, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However for quantum dynamical systems like quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input which may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators and the connection to large deviations is briefly discussed. 1
Maximum likelihood versus likelihoodfree quantum system identification in the atom maser. arXiv:1311.4091
, 2013
"... the atom maser ..."
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EQUIVALENCE CLASSES AND LOCAL ASYMPTOTIC NORMALITY IN SYSTEM IDENTIFICATION FOR QUANTUM MARKOV CHAINS
"... Abstract. We consider the problems of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. On the identifiability question, we show that the knowledge of the output state completely fixes the dynamics up t ..."
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Abstract. We consider the problems of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. On the identifiability question, we show that the knowledge of the output state completely fixes the dynamics up to a ‘coordinate transformation’ consisting of a multiplication by a phase and a unitary conjugation of the Kraus operators. When 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. 1.
The operators P and Q 1.1 The Hilbert space
, 2011
"... A teljes könyv címe: An invitation to the algebra of the canonical commutation relation ..."
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A teljes könyv címe: An invitation to the algebra of the canonical commutation relation
Local asymptotic normality for finite . . .
, 2008
"... The previous results on local asymptotic normality (LAN) for qubits [20, 17] are extended to quantum systems of arbitrary finite dimension d. LAN means that the quantum statistical model consisting of n identically prepared ddimensional systems with joint state ρ⊗n converges as n → ∞ to a statisti ..."
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The previous results on local asymptotic normality (LAN) for qubits [20, 17] are extended to quantum systems of arbitrary finite dimension d. LAN means that the quantum statistical model consisting of n identically prepared ddimensional systems with joint state ρ⊗n converges as n → ∞ to a statistical model consisting of classical and quantum Gaussian variables with fixed and known covariance matrix, and unknown means related to the parameters of the density matrix ρ. Remarkably, the limit model splits into a product of a classical Gaussian with mean equal to the diagonal parameters, and independent harmonic oscillators prepared in thermal equilibrium states displaced by an amount proportional to the offdiagonal elements. As in the qubits case [17], LAN is the main ingredient in devising a general two step adaptive procedure for the optimal estimation of completely unknown ddimensional quantum states. This measurement strategy shall be described in a forthcoming paper [19].