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

Abstract

We address the quantum metrology for two modes of a Dirac field described by relatively accelerated parties. By using the quantum Fisher information (QFI), we investigate how the weak measurements performed before and after the accelerating observer, affect the optimal estimation of information encoded into the weight and phase parameters of the initial state shared between the parties. Studying the QFI, associated with weight parameter ϑ, we find that the acceleration at which the optimal estimation occurs may be controlled by weak measurements. Moreover, it is shown that the post-measurement plays the role of a quantum key for manifestation of the Unruh effect. On the other hand, investigating the phase estimation optimization and assuming that there is no control over the initial state, we show that the weak measurements may be utilized to match the optimal ϑ to its predetermined value. Moreover, in addition to determination of a lower bound on the QFI with the local quantum uncertainty in the presence of Unruh effect, we unveil an important upper bound on the precision of phase estimation, given by the maximal steered coherence (MSC). We also obtain a compact expression of the MSC for general X states.

Multiparameter estimation, lower bound on quantum Fisher information, and non-Markovianity witnesses of noisy two-qubit systems

“…We remark that the QFIs are obtained from the output estimation data, while the LQU or IP is measured on the input probe states. On the other hand, for few special open quantum systems, i.e., two coupled qubits interacting with the independent non-Markovian Lorentzian form environments (59) and two modes of a Dirac field described by relatively accelerated parties (60), it has been illustrated that the LQU of the evolved state is majorized by the QFI associated with the phase parameter encoded into the initial state of the system. It is also interesting to investigate how the evolved state IP of the open quantum system can be employed to investigate the multi-parameter estimation and metrological scaling associated with the initial state of the system.…”

Quantum thermometry in a squeezed thermal bath

“…The classical approach to decrease the statistical error is increase in the the resources for the measurement according to the central limit theorem; but this method is not always desirable or efficient [2]. Quantum parameter estimation theory describes strategies allowing the estimation precision to surpass the limit of classical approaches [3][4][5][6][7][8][9][10][11][12]. When the quantum system is sampled N times, different strategies [13] allowing one to achieve the Heisenberg limit, can be designed such that the variance of the estimated parameter scales as 1/N 2 .…”