Abstract
The nonunital non-Markovian dynamics of qubits immersed in a spin bath is studied without any Markovian approximation. The environmental effects on the precisions of quantum parameter estimation are taken into account. The time-dependent transfer matrix and inhomogeneity vector are obtained for the description of the open dynamical process. The dynamical behaviour of one qubit coupled to a spin bath is geometrically described by the Bloch vector. It is found out that the nonunital non-Markovian effects can engender the improvement of the precision of quantum parameter estimation. This result contributes to the environment-assisted quantum information theory.
Highlights
The open dynamical process can be regarded as Markovian dynamics in the weak coupling approximation where the correlation time of the bath is much smaller than the decay time of the open system
The nonunital non-Markovian effects from the environment can be studied by the timedependent transfer matrix and inhomogeneity vector which are determined by the decoherence factors
The nonunital non-Markovian dynamics of the open system in a spin bath is analytically obtained in the thermodynamics limit by using the special operator method
Summary
There are always energy or information exchanges between open quantum systems and environments, owing to external measurements and inherent spontaneous decays.[1,2] The open dynamical process can be regarded as Markovian dynamics in the weak coupling approximation where the correlation time of the bath is much smaller than the decay time of the open system. Many useful measures on the non-Markovian degree for a dynamical map have been suggested in the recent years.[23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38] The measures based on distance fidelity,[23,24,39,40] entanglement,[25] indivisibility,[26] quantum discord[27] and Fisher information[28] are applied to quantitatively evaluate some non-Markovian dynamics such as dephasing channel and general amplitude-damping one.
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