Abstract
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
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
Original language  English 

Pages (fromto)  1397–1428 
Number of pages  32 
Journal  Communications in Mathematical Physics 
Volume  335 
Issue number  3 
Early online date  26 Nov 2014 
DOIs  
Publication status  Published  31 May 2015 
Externally published  Yes 
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Jukka Kiukas
Person: Teaching And Research