Abstract We investigate precision of phase estimation without and with decoherence using a non-Hermitian operation, i.e. parity-time ( ) symmetric operation. We derive the exact expressions of the optimal quantum Fisher information (QFI) and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. Special attention is paid to the two schemes, i.e. pre-and post- symmetric operations, to show the performance of symmetric operation on QFI dynamics. By investigation, we find that pre- symmetric operator process could completely eliminate the effect of decoherence to improve the parameters estimation, while with the help of the post- symmetric operator process can potentially enhance and preserve the QFI by choosing appropriate non-Hermitian operator parameters.
Abstract The enhancement of the precision of phase estimation in quantum metrology is investigated by employing parity-time ( P T ) symmetric operation. We derive the exact expressions of the quantum Fisher information (QFI) and the success probability of the phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. Special attention is paid to the two schemes, i.e. pre-and post- P T symmetric operations. We show that the QFI can be obviously enhanced by means of the P T symmetric operation in different regimes. In addition, we also show that the magnitude of the decoherence involved in the P T symmetric operation can be a general complex number, which extends the applicable scope of the P T symmetric operation approach.
Recently, Zhong et al. [Phys. Rev. A 87, 022337(2013)] investigated the dynamics of quantum Fisher information (QFI) in the presence of decoherence. We here reform their results and propose two schemes to enhance and preserve the QFIs for a qubit system subjected to a decoherence noisy environment by applying
non-Hermitian operators process. The proposed schemes are related to the
prior (or the
post ) non-Hermitian operator process corresponding to before (or after) the interest system suffers from decoherence, respectively. Resorting to the Bloch sphere representation, we derive the exact analytical expressions of the QFIs with respect to the amplitude parameter
θ and the phase parameter
ϕ, and in detail investigate the influence of
non-Hermitian operator parameters on the QFIs. Compared with purity decoherence process (without non-Hermitian operator process), we find that the
post non-Hermitian operator process can potentially enhance and preserve the QFIs by choosing appropriate
non-Hermitian operator parameters, while with the help of the
prior non-Hermitian operator process one could completely eliminate the effect of decoherence to improve the parameters estimation. Finally, a generalized non-Hermitian operator parameters effect on the parameters estimation is also considered.
Abstract In this work, we investigate effect of parity-time ( PT ) symmetric operation on the dynamic behavior of entanglement for two qubits system in Markovian and non-Markovian regimes with the resonant and off-resonant cases. First we derive the explicit expressions of concurrence quantifying entanglement for an exactly solving model consisting of two qubits interacting with independent structured reservoir. Then, we give two schemes, i.e. pre- and post- PT symmetric operations, to show the performance of PT symmetric operation on entanglement dynamics of two qubits. By investigation, we find that the lower the absolute value of the PT operation strength, the better the enhancement of entanglement. In addition, we show that the entanglement can be obviously enhanced by means of the pre- PT symmetric operation in different regimes.
The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement (WM) and quantum measurement reversal (QMR). We derive the exact expressions of the optimal quantum Fisher information (QFI) and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.
Abstract The dynamic behavior of the relative entropy of coherence for a two-level system is systematically investigated within non-Markovian environment. We derive the exact expressions of relative entropy quantifying coherence for an exactly solving model consisting of single qubit interacting with independent structured reservoir. By employing local non-Hermitian operation, i.e. parity-time ( PT ) symmetric operation, we show that the vanished quantum coherence can be effectively restored under the non-Markovian regimes. Furthermore, the freezing phenomenon of the coherence can be detected by using the optimal PT symmetric operation strength within the non-Markovian environments.
Quantum parameter estimation with Hermitian systems has been applied in various fields, but there are relatively few results concerning non-Hermitian systems. Here, we study the quantum parameter estimation for general non-Hermitian Hamiltonians and derive an intuitive expression of quantum Fisher information (QFI) for pure states. Furthermore, we propose the condition for optimal measurements, which is applicable to both Hermitian and non-Hermitian Hamiltonians. To illustrate these results, we calculate and study the QFI of a specific parity-time
(PT) -symmetric non-Hermitian Hamiltonian and give the optimal measurement. Surprisingly, we find some interesting properties of this
PT-symmetric Hamiltonian QFI, such as the mutations in QFI at exceptional point. Moreover, we also compare the variance of estimation generated by the optimal measurement with the theoretical precision bound to verify the condition for optimal measurements we proposed.