Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment

Abstract

Quantum Fisher information (QFI) is an important feature for the precision of quantum parameter estimation based on the quantum Cramér-Rao inequality. When the quantum state satisfies the von Neumann-Landau equation, the local quantum uncertainty (LQU), as a kind of quantum correlation, present in a bipartite mixed state guarantees a lower bound on QFI in the optimal phase estimation protocol [Phys. Rev. Lett. 110 (2013) 240402]. However, in the open quantum systems, there is not an explicit relation between LQU and QFI generally. In this paper, we study the relation between LQU and QFI in open systems which is composed of two interacting two-level systems coupled to independent non-Markovian environments with the entangled initial state embedded by a phase parameter θ. The analytical calculations show that the QFI does't depend on the phase parameter θ, and its decay can be restrained through enhancing the coupling strength or non-Markovianity. Meanwhile, the LQU is related to the phase parameter θ and shows plentiful phenomena. In particular, we find that the LQU can well bound the QFI when the coupling between the two systems is switched off or the initial state is Bell state.

Quantum acceleration by an ancillary system in non-Markovian environments

“…The quantum speed limit time can be significantly decreased along with the increasing of the environment coupling parameters γ 0 and hopping interaction J, and demonstrates stronger periodic oscillation phenomenon. The similar property can also be found in the dynamics of the quantum correlation [47] based on the skew information [48,49]. For the dynamics of the system, one should notice that it can not be reduced to the damped Jaynes-Cummings model when the hopping interaction J is zero.…”

“…Substituting the quantum state |ψ id (t) into the Schrödinger equation i ∂ t | ψid (t) = H|ψ id (t) , one can obtain the differential equations for the coefficients A id (t), B id (t), C k id (t) and D k id (t) [47]:…”

Weak measurement effect on optimal estimation with lower and upper bound on relativistic metrology

“…It should be noted that in this model, the other steps of the estimation process are assumed to be noiseless. Besides, in (36), it has been shown that for a model, consisting of two qubits interacting with independent non-Markovian environments, when we consider the effects of the environment and the coupling interaction between subsystems, the QFI and LQU do not satisfy the similar relationship generally. Now we investigate whether or not this bound holds for our model including the PM's and the Unruh effect.…”

“…9(a)-9(d) for determined values of other parameters, equality F ϕ = U A (ρ A,I ) holds. Moreover, inequality (36) refers to the fact that the quantum correlations measured by LQU, are a sufficient resource to ensure that some information about the phase parameter can be extracted from the system in the process of estimation. In addition, for probe quantum states with any nonzero amount of discord, and for M ≫ 1 repetitions of the estimation process, the optimal detection strategy, asymptotically saturating the quantum Cramér-Rao bound, leads to production of an estimator φbest with the following necessarily limited variance:…”

“…Moreover, Ref. (36) has been studied the relationship between the QFI and the LQU in a special open quantum system involving two coupled qubits interacting with the independent non-Markovian Lorentzian form environments.…”