The force estimation problem in Quantum Metrology with an arbitrary non-Markovian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state and the best measurement. We emphasis the effects of the non-Markovian bath by studying the short time behavior and find out the essence of non-Markovian effects such as increase in quantum Fisher information. We show that at this time scale the non-Markovian dynamics is much closer to the free dynamics than the Markovian equivalent. This brings huge consequences for the sequential measurement as the quantum Fisher information becomes unbounded when the initial probe mean energy goes to infinity, whereas its Markovian counterpart remains bounded by a constant. The long time behavior shows the complexity and potential variety of non-Markovian effects, somewhere between the exponential decay characteristic of Markovian dynamics and the sinusoidal oscillations characteristic of resonant narrow band.
The force estimation problem in Quantum Metrology with an arbitrary non-Markovian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state and the best measurement. We emphasis the effects of the non-Markovian bath by studying the short time behavior and find out the essence of non-Markovian effects such as increase in quantum Fisher information. We show that at this time scale the non-Markovian dynamics is much closer to the free dynamics than the Markovian equivalent. This brings huge consequences for the sequential measurement as the quantum Fisher information becomes unbounded when the initial probe mean energy goes to infinity, whereas its Markovian counterpart remains bounded by a constant. The long time behavior shows the complexity and potential variety of non-Markovian effects, somewhere between the exponential decay characteristic of Markovian dynamics and the sinusoidal oscillations characteristic of resonant narrow band.
The force estimation problem in quantum metrology with an arbitrary non-Markovian Gaussian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states, we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state, and the best measurement. Studying the short-time behavior and comparing with regular Markovian dynamics we observe an increase in quantum Fisher information. We emphasize that this phenomenon is due to the ability to perform measurements below the correlation time of the bath, activating non-Markovian effects. This brings huge consequences for the sequential preparation-and-measurement scenario because the quantum Fisher information becomes unbounded when the initial probe mean energy goes to infinity, whereas its Markovian counterpart remains bounded by a constant. The long-time behavior shows the complexity and potential variety of non-Markovian effects, somewhere between the exponential decay characteristic of Markovian dynamics and the sinusoidal oscillations characteristic of resonant narrow bands.
The problem of quantum metrology in the context of a particular non-Markovian quantum evolution is explored. We study the dynamics of the quantum Fisher information (QFI) of a composite quantum probe coupled to a Lorentzian environment, for a full variety of different classes of parameters. We are able to find the best metrological state, which is not maximally entangled but is the one which evolves the most rapidly. This is shown by demonstrating a connection between QFI and different quantum speed limits. At the same time, by optimizing a control field acting on the probes, we show how the total information flow is actively manipulated by the control so as to enhance the parameter estimation at a given final evolution time. Finally, under this controlled scenario, a sharp interplay between the dynamics of QFI, non-Markovianity, and entanglement is revealed within different control schemes.
We consider a metrology scenario in which qubit-like probes are used to sense an external field that affects their energy splitting in a linear fashion.Following the frequency estimation approach in which one optimizes the state and sensing time of the probes to maximize the sensitivity, we provide a systematic study of the attainable precision under the impact of noise originating from independent bosonic baths.Specifically, we invoke an explicit microscopic derivation of the probe dynamics using the spin-boson model with weak coupling of arbitrary geometry.We clarify how the secular approximation leads to a phase-covariant (PC) dynamics, where the noise terms commute with the field Hamiltonian, while the inclusion of non-secular contributions breaks the PC.Moreover, unless one restricts to a particular (i.e., Ohmic) spectral density of the bath modes, the noise terms may contain relevant information about the frequency to be estimated.Thus, by considering general evolutions of a single probe, we study regimes in which these two effects have a non-negligible impact on the achievable precision.We then consider baths of Ohmic spectral density yet fully accounting for the lack of PC, in order to characterize the ultimate attainable scaling of precision when N probes are used in parallel.Crucially, we show that beyond the semigroup (Lindbladian) regime the Zeno limit imposing the 1/N 3/2 scaling of the mean squared error, recently derived assuming PC, generalises to any dynamics of the probes, unless the latter are coupled to the baths in the direction perfectly transversal to the frequency encoding-when a novel scaling of 1/N 7/4 arises.As our microscopic approach covers all classes of dissipative dynamics, from semigroup to non-Markovian ones (each of them potentially non-phase-covariant), it provides an exhaustive picture, in which all the different asymptotic scalings of precision naturally emerge.
Accurately characterizing the properties of structured reservoirs is a key challenge in quantum systems and is of great importance for advances in quantum metrology and sensing. In this work, we employ a two-level system (qubit) as a probe, which is coupled to a structured reservoir consisting of an ancilla qubit and a Markovian environment modeled as a thermal bath. By exploiting non-Markovian dynamics, we systematically investigate the effectiveness of different interaction types between the probe and ancilla for estimating critical parameters, including temperature, ancilla frequency, and system-bath coupling strength. We quantify the precision of parameter estimation using quantum Fisher information (QFI) and analyze the system dynamics in both transient and steady-state regimes. Our findings demonstrate that non-Markovianity substantially enhances parameter estimation in the transient regime, with specific interactions facilitating sustained information backflow and yielding higher QFI values. However, the performance of these interactions is contingent on the parameter under estimation and the operational regime. For instance, certain interactions become prominent in the transient regime but exhibit diminished utility in the steady state, whereas others maintain their effectiveness even at equilibrium. These results stress the importance of judiciously selecting interactions adapted to specific estimation objectives and operational regimes.
Quantum metrology utilizes quantum effects to reach higher-precision measurements of physical quantities compared with their classical counterparts. However, the ubiquitous decoherence obstructs its application. Recently, non-Markovian effects are shown to be effective in performing quantum optical metrology under locally dissipative environments [Phys. Rev. Lett. 123, 040402 (2019)]. However, the mechanism is still rather hazy. Here, we uncover the reason why forming a bound state can protect the quantumness against a dissipative ambient via the quantum Fisher information of entangled coherent states. An exact analytical expression of the quantum Fisher information in the long-encoding-time condition is derived, which reveals that the dynamics of precision can asymptotically reach the ideal-case-promised one easily when the average photon number is small. Meanwhile, the scaling exhibits a transition from the weak Heisenberg limit to the subclassical limit with increasing average photon number. Our work provides a recipe to realize ultrasensitive measurements in the presence of noise by utilizing non-Markovian effects.
We explore the nonunital non-Markovian dynamics of a qubit immersed in a spin bath. The nonunital environmental effects on the precisions of quantum parameter estimation are investigated. The time-dependent transfer matrix and inhomogeneity vector are obtained for the description of the open dynamical process. The evolution of the coherent vectors for a qubit is studied so as to geometrically demonstrate the nonunital non-Markovian effects. The revivals of angles for the fidelity between a maximal mixed state and an arbitrary trajectory state are presented in the nonunital non-Markovian dynamics. The degree for the nonunitality is controllable with the changes of the local magnetic field for a qubit and spin bath temperature. It is found out that the increase of quantum Fisher information for composite states is connected with the nonunital non-Markovian effects, which is helpful for the improvement of quantum metrology.