Quantum Fisher information of an open and noisy system in the steady state

We study the quantum Fisher information (QFI) per particle of an open (particles can enter and leave the system) and dissipative (far from thermodynamical equilibrium) steady state system of two qubits in a noise which is decoherence. We show the behavior of QFI per particle of the system due to changes of reset and decoherence parameters rr and γγ respectively. The parameter rr is the strength of the reset mechanism, γγ is the strength of decoherence and in our case it is dephasing channel. The parameters γγ and rr are real numbers. We observe that the reset parameter must be bigger than decoherence parameter. We have found that by choosing coupling parameter gg as 5γ5γ the QFI per particle is 1.00226 which is greater than shot noise limit at γ=0.5γ=0.5 and r=14r=14. Also the concurrence and negativity of the such state have been calculated and they are found as 0.0992486 and 0.0496243 respectively. We have shown that when the concurrence and negativity of some specific states different than zero, which means the state is entangled, the QFI of the system is greater than 1. The QFI per particle, concurrence and negativity shows that the chosen case is weakly entangled. We discovered that the optimal direction depends on the parameters rr and γγ and a change in the direction affects the behavior of the QFI of the system.