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Chinese Physics B

Optimal quantum parameter estimation of two-qutrit HeisenbergXYchain under decoherence

Hongying Yang, Qiang Zheng, Qi‐Jun Zhi

Published Jan 1, 2017• 5 citations
Publisher

Abstract

Adopting the Milburn decoherence model, we investigate the performance of quantum Fisher information of the two-qutrit isotropic Heisenberg XY chain under decoherence. We find that the quantum Fisher information with respect to the decoherence rate and the magnetic field decreases exponentially in the long-time limit, which significantly reduces the precision of optimal quantum estimation. We also show that with the increase of the decoherence rate or the magnetic field, the QFIs go down considerably. Furthermore, we find that the precision of optimal quantum estimation can be enhanced by the entanglement in the input state.

DOI
10.1088/1674-1056/26/1/010601

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Adopting the Milburn decoherence model, we investigate the performance of quantum Fisher information of the two-qutrit isotropic Heisenberg XY chain under decoherence. We find that the quantum Fisher information with respect to the decoherence rate and the magnetic field decreases exponentially in the long-time limit, which significantly reduces the precision of optimal quantum estimation. We also show that with the increase of the decoherence rate or the magnetic field, the QFIs go down considerably. Furthermore, we find that the precision of optimal quantum estimation can be enhanced by the entanglement in the input state.
We theoretically investigate quantum parameter estimation in a two-qubit anisotropic Heisenberg spin system with Dzyaloshinskii-Moriya (DM) interaction in the presence of intrinsic decoherence described by the Milburn model. Using the Quantum Fisher Information (QFI), we study the estimation of both the uniform magnetic field and the DM interaction strength. Analytical expressions for the time-evolved density matrix are obtained and used to explore the effects of exchange anisotropy, intrinsic decoherence, and probe-state preparation on the achievable estimation precision. Our results show that suitable tuning of the anisotropic exchange coupling and the initial entangled state can considerably enhance the estimation performance, with different optimal parameter regimes emerging for magnetic-field and DM-interaction sensing. To better understand the role of quantum resources in metrology, we also examine the behaviour of concurrence, quantum coherence, and von Neumann entropy. Overall, our findings demonstrate that anisotropic Heisenberg spin systems with DM interaction provide a promising and flexible platform for high-precision quantum metrology even in the presence of intrinsic decoherence.
We investigate the parameter estimation problem in a two-qubit system, in which each qubit is independently interacting with its Markovian environment. We study in detail the sensitivity of the estimation on the decoherence rate γγγ and the two-qubit interaction strength vvv. In particular, the dynamics of quantum Fisher information are employed as a measure to quantify the precision of the estimations. We find that the quantum Fisher information with respect to the decoherence rate scales like t2/[exp⁡(γt)−1]t^2/[\exp(γt)-1]t2/[exp(γt)−1] and exp⁡(−2γt)\exp(-2γt)exp(−2γt) in the unitary limit and the completely decoherent limit, respectively. When we estimate the interaction strength vvv, the quantum Fisher information shows oscillation behavior in term of time. In addition, our results provide further evidence that the entanglement of the input state may not enhance quantum metrology.
Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a Hamiltonian can be increased to exceed the classical limit, yet little is known about estimating a general Hamiltonian parameter. In this paper, we study this problem in detail. We find that the scaling of the estimation precision with the number of systems can always be optimized to the Heisenberg limit, while the time scaling can be quite different from that of estimating an overall multiplicative factor. We derive the generator of local parameter translation on the unitary evolution operator of the Hamiltonian, and use it to evaluate the estimation precision of the parameter and establish a general upper bound on the quantum Fisher information. The results indicate that the quantum Fisher information generally can be divided into two parts: one is quadratic in time, while the other oscillates with time. When the eigenvalues of the Hamiltonian do not depend on the parameter, the quadratic term vanishes, and the quantum Fisher information will be bounded in this case. To illustrate the results, we give an example of estimating a parameter of a magnetic field by measuring a spin-12\frac{1}{2}21​ particle and compare the results for estimating the amplitude and the direction of the magnetic field.
We employ the concepts of quantum Fisher information, quantum coherence, and fidelity to study a thermally environmental effect on the teleportation process. It is assumed that a single qutrit is teleported through a thermally environmental containing a two-qutrit Heisenberg XX chain under the external magnetic field (EMF) and Dzyaloshinski Moriya (DM) interaction. The energy spectrum of the physical Hamiltonian and its eigenstates are employed to obtain the thermal density matrix, which is used as a thermal teleportation environment. The Resort to the definition of quantum Fisher information for a single qubit system, we estimate the optimal behaviour concerning the EMF and temperature. The result shows that maximizing the estimation degree depends on increasing the EMF and minimizing it requires lowering temperature. The effect of temperature and DM coupling on the quantum coherence and fidelity of the teleported state is studied. It is shown that temperature destroyed the maximum bounds of the two physical quantity, while the DM coupling delays the effect of EMF at the same periods.
Various schemes have been proposed to overcome the drawback of the decoherence on quantum-enhanced parameter estimation. Here we suggest an alternative method, quantum feedback, to enhance the parameter precision of optimal quantum estimation of a dissipative qubit by investigating its dynamics of quantum Fisher information. We find that compared with the case without feedback, the quantum Fisher information of the dissipative qubit in the case of feedback has a large maximum value in time evolution and a smaller decay rate in the long time.
Abstract The precision of measurements for two incompatible observables in a physical system can be improved with the assistance of quantum memory. In this paper, we investigate the quantum-memory-assisted entropic uncertainty relation for a spin-1 Heisenberg model in the presence of external magnetic fields, the systemic quantum entanglement (characterized by the negativity) is analyzed as contrast. Our results show that for the XY spin chain in thermal equilibrium, the entropic uncertainty can be reduced by reinforcing the coupling between the two particles or decreasing the temperature of the environment. At zero-temperature, the strong magnetic field can result in the growth of the entropic uncertainty. Moreover, in the Ising case, the variation trends of the uncertainty are relied on the choices of anisotropic parameters. Taking the influence of intrinsic decoherence into account, we find that the strong coupling accelerates the inflation of the uncertainty over time, whereas the high magnetic field contributes to its reduction during the temporal evolution. Furthermore, we also verify that the evolution behavior of the entropic uncertainty is roughly anti-correlated with that of the entanglement in the whole dynamical process. Our results could offer new insights into quantum precision measurement for the high spin solid-state systems.