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.
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 Non‐Hermitian systems have attracted increasing attention in recent years, particularly those exhibiting Parity‐Time (PT) symmetry. Quantum metrology establishes the ultimate attainable bounds for parameter estimation in both Hermitian and non‐Hermitian systems. However, comparatively little is known about non‐Hermitian systems with anti‐Parity‐Time (APT) symmetry. In this work, we investigate the theoretical bounds on quantum parameter estimation precision for an APT‐symmetric system governed by the Bogoliubov–de Gennes (BdG) Hamiltonian. We explicitly derive the expression for the quantum Fisher information (QFI) and compare the attainable precision limits for both multiplicative and non‐multiplicative parameters in the BdG Hamiltonian. Our analysis of the effective QFI reveals that quantum parameter estimation precision can be significantly enhanced as the system approaches the exceptional point with unbroken APT symmetry, where Heisenberg scaling becomes achievable. We also examine how the effective QFI depends on the choice of initial states. Furthermore, we demonstrate that entanglement in multi‐particle initial state can provide an additional enhancement to the QFI. The ratio of limit of parameter estimation precision of the entangled state to the greatest one we have found over all the tensor product states is 1.22, which is greater than 1. Our analysis of two‐particle states confirms that entanglement in the initial state can further increase the QFI, highlighting it as a valuable quantum resource. These findings lay a theoretical foundation for future experimental explorations of parameter estimation in APT‐symmetric non‐Hermitian systems.
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.
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.
We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information (QFI) yields results that are asymptotically equivalent to those from the rigorous Bayesian approach, provided generic uncorrelated noise is present in the setup. At the same time, we show that for the problem of decoherence-free phase estimation this equivalence breaks down, and the achievable estimation uncertainty calculated within the Bayesian approach is larger by a factor of π than that predicted from the QFI even in the large prior knowledge (small parameter fluctuation) regime, where the QFI is conventionally regarded as a reliable figure of merit. We conjecture that an analogous discrepancy is present in the arbitrary decoherence-free unitary parameter estimation scheme, and propose a general formula for the asymptotically achievable precision limit. We also discuss protocols utilizing states with an indefinite number of particles, and show that within the Bayesian approach it is legitimate to replace the number of particles with the mean number of particles in the formulas for the asymptotic precision, which as a consequence provides another argument for proposals based on the properties of the QFI of indefinite particle number states leading to sub-Heisenberg precisions not being practically feasible.