Abstract
In this paper, our prime objective is to apply the techniques of parameter estimation theory and the concept of Quantum Metrology in the form of Fisher Information to investigate the role of certain physical quantities in the open quantum dynamics of a two entangled qubit system under the Markovian approximation. There exist various physical parameters which characterize such system, but can not be treated as any quantum mechanical observable. It becomes imperative to do a detailed parameter estimation analysis to determine the physically consistent parameter space of such quantities. We apply both Classical Fisher Information (CFI) and Quantum Fisher Information (QFI) to correctly estimate these parameters, which play significant role to describe the out-of-equilibrium and the long range quantum entanglement phenomena of open quantum system. Quantum Metrology, compared to classical parameter estimation theory, plays a two-fold superior role, improving the precision and accuracy of parameter estimation. Additionally, in this paper we present a new avenue in terms of Quantum Metrology, which beats the classical parameter estimation. We also present an interesting result of revival of out-of-equilibrium feature at the late time scales, arising due to the long range quantum entanglement at early time scale and provide a physical interpretation for the same in terms of Bell's Inequality Violation in early time scale giving rise to non-locality.
Highlights
Our prime objective is to apply the techniques of parameter estimation theory and the concept of Quantum Metrology in the form of Fisher Information to investigate the role of certain physical quantities in the open quantum dynamics of a two entangled qubit system under the Markovian approximation
We present an interesting result of revival of out-of-equilibrium feature at the late time scales, arising due to the long range quantum entanglement at early time scale and provide a physical interpretation for the same in terms of Bell’s Inequality Violation in early time scale giving rise to non-locality
In section Estimation of Parameters : Estimation of TimeScale, Estimation of Euclidean Distance, Estimation of Coupling Strength we apply the techniques of Fisher Information, both Classical and Quantum to estimate some of the essential physical parameters that plays a pivotal role in determining the time evolutionary dynamics of the system under consideration
Summary
We review a model of two identical entangled qubits as described with much clarity in [5]. The system of two entangled qubits is described by the linear combinations of the contributions coming from the individual qubit and is described by the following Hamiltonian: HS In this construction, ω, ω0 and the factor k which is appearing in the Fourier transform of the Wightman functions (see appendix) all are taken real to perform the Fisher Information analysis in this paper and this is necessarily required to suffice the present purpose. To have a better understanding of the system and to estimate the parameters, we must solve the GSKL Master Equation For this purpose, we parametrize our arbitrary two qubit subsystem density matrix in terms of Pauli matrices by the following expression: ρS ( t ). ∂ ∂ ξa denoting the partial differentiation with respect to the desired parameter (here, ξa) In this context, Fab forms a matrix called Quantum Fisher Information Matrix (QFIM). From the above argument it is clear that the Fisher Information of a pure state is generally greater than that of a mixed state
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