Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems

Hilbert–Schmidt speed (HSS) is a special type of quantum statistical speed which is easily computable, since it does not require diagonalization of the system state. We find that, when both HSS and quantum Fisher information (QFI) are calculated with respect to the phase parameter encoded into the initial state of an n-qubit register, the zeros of the HSS dynamics are actually equal to those of the QFI dynamics. Moreover, the signs of the time-derivatives of both HSS and QFI exactly coincide. These findings, obtained via a thorough investigation of several paradigmatic open quantum systems, show that HSS and QFI exhibit the same qualitative time evolution. Therefore, HSS reveals itself as a powerful figure of merit for enhancing quantum phase estimation in an open quantum system made of n qubits. Our results also provide strong evidence for both contractivity of the HSS under memoryless dynamics and its sensitivity to system-environment information backflows to detect the non-Markovianity in high-dimensional systems, as suggested in previous studies

Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-) PT -symmetric systems

Non-Hermitian systems with parity-time (PT) symmetry and anti-PT symmetry lead to exceptional points (EPs) with intriguing properties related to, e.g., chiral transport and enhanced sensitivity, due to the coalescence of eigenvectors. In this paper, we propose an easily computable tool, based on the Hilbert–Schmidt speed (HSS), not requiring the diagonalization of the evolved density matrix, to detect exactly the EPs, especially in high-dimensional systems. Our theoretical predictions, made without the need for modification of the Hilbert space, are completely consistent with results extracted from recent experiments studying the criticality in (anti-)PT-symmetric systems. Moreover, not modifying the Hilbert space of the non-Hermitian system, we find that the trace distance whose dynamics is known as a faithful witness of non-Markovianity, may be non-contractive under the non-Hermitian evolution of the system. Therefore, it losses one of the most important characteristics which must be met by any standard witness of non-Markovianity. We also address the non-contractivity of quantum Fisher information in non-Hermitian systems

Relation between Berry phases and entanglement besides convergence of levels for two entangled spin-1/2 particles in magnetic fields

We study the effects of an extra static magnetic field, coupling with one of the two entangled spin-1/2 particles, on Berry phases and entanglement of the adiabatic eigensatates of the system, while the other spin interacts with a rotating magnetic field satisfying the adiabatic condition. This static magnetic field can be used for controlling the Berry phases and the entangled state of the system. The relation of the Berry phases and entanglement to Dzyaloshinski-Moriya interaction, coupling coefficient, and the magnetic fields are also investigated. The results demonstrate a close relationship between the Berry phases and pairwise entanglement (as measured by the so-called entanglement of formation). We show that reversing the sign of the static magnetic field can cause exchanges of the Berry phases and entanglement between the adiabatic states. It is illustrated that the geometric phases and entanglement are good indicators to detect the convergence of the levels and each convergence of levels corresponds to abrupt changes in the Berry phases and entanglement

Relativistic quantum thermometry through a moving sensor

Using a two-level moving probe, we address the temperature estimation of a static thermal bath modeled by a massless scalar field prepared in a thermal state. Different couplings of the probe to the field are discussed under various scenarios. We find that the thermometry is completely unaffected by the Lamb shift of the energy levels. We take into account the roles of probe velocity, its initial preparation, and environmental control parameters for achieving optimal temperature estimation. We show that a practical technique can be utilized to implement such a quantum thermometry. Finally, exploiting the thermal sensor moving at high velocity to probe temperature within a multiparameter-estimation strategy, we demonstrate perfect supremacy of the joint estimation over the individual one

Memory Effects in High-Dimensional Systems Faithfully Identified by Hilbert\u2013Schmidt Speed-Based Witness

A witness of non-Markovianity based on the Hilbert\u2013Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful, being easily computable since no diagonalization of the system density matrix is required. We investigate the sensitivity of this HSS-based witness to detect non-Markovianity in various high-dimensional and multipartite open quantum systems with finite Hilbert spaces. We find that the time behaviors of the HSS-based witness are always in agreement with those of quantum negativity or quantum correlation measure. These results show that the HSS-based witness is a faithful identifier of the memory effects appearing in the quantum evolution of a high-dimensional system with a finite Hilbert space