An obstacle for precision improvement in quantum metrology is the information loss causing by the unavoidable interaction between probe system and environment. Quantum fluctuations are environment no system can be isolated from and it will make the precision of initial parameter estimation of the probe atom decrease with time. After the typical time of the spontaneous decay of the probe atom, the precision is greatly damaged. However, quantum fluctuations can be modified. Our results show that if we put several ancillary atoms beside the probe atom in symmetrical arrangement, the probe atom will be affected by the ancillary atoms indirectly and the information loss of the probe atom causing by the quantum fluctuations will be partially avoided. We find that the retained precision after long time evolution can approaches to [Formula: see text] times of the initial precision in condition that the probe atom and three ancillary atoms are located in the vertex of regular tetrahedron.
An obstacle for precision improvement in quantum metrology is the information loss causing by the unavoidable interaction between probe system and environment. Quantum fluctuations are environment no system can be isolated from and it will make the precision of initial parameter estimation of the probe atom decrease with time. After the typical time of the spontaneous decay of the probe atom, the precision is greatly damaged. However, quantum fluctuations can be modified. Our results show that if we put several ancillary atoms beside the probe atom in symmetrical arrangement, the probe atom will be affected by the ancillary atoms indirectly and the information loss of the probe atom causing by the quantum fluctuations will be partially avoided. We find that the retained precision after long time evolution can approaches to [Formula: see text] times of the initial precision in condition that the probe atom and three ancillary atoms are located in the vertex of regular tetrahedron.
The Heisenberg scaling is an ultimate precision limit of parameter estimation allowed by the principles of quantum mechanics, with no counterpart in the classical realm, and has been a long-pursued goal in quantum metrology. It has been known that interactions between the probes can help reach the Heisenberg scaling without entanglement. In this paper, we show that interactions between the probes and the additional dimensions of an ancillary system may also increase the precision of parameter estimation to surpass the standard quantum limit and attain the Heisenberg scaling without entanglement, if the measurement scheme is properly designed. The quantum Fisher information exhibits periodic patterns over the evolution time, implying the existence of optimal time points for measurements that can maximize the quantum Fisher information. By implementing optimizations over the Hamiltonian, the initial states of the probes and the ancillary system, the interaction strength, and the time points for measurements, our protocol achieves the Heisenberg scaling for the parameter of the probe Hamiltonian, in terms of both evolution time and probe number. Our protocol features two aspects: (i) the Heisenberg scaling can be achieved by a product state of the probes and (ii) mere local measurement on the ancilla is sufficient, both of which reduce the quantum resources and the implementation complexity to achieve the Heisenberg scaling. The paper is concluded by the investigation of the effects of noise on this protocol.
Abstract The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcomewhen using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining general precision bounds in the presence of an environment.We adopt a complementary approach,wherewe first analyze the problem within the general framework of describing the quantum systems in terms of quantum dynamical maps and then relate this abstract formalism to a microscopic description of the system’s dissipative time evolution.We will show that although some forms of noise do render quantum systems standard quantum limited, precision beyond classical bounds is still possible in the presence of different forms of local environmental fluctuations.
One of the most concerned problems in quantum metrology is exploiting quantum resources to increase the precision of quantum parameter estimation. One natural and standard way of improving the precision of estimation is letting the initial probe state being optimal. However, the optimal initial probe state on the one hand may be hard to identify, and on the other hand one cannot prepare the optimal initial state perfectly in practice. In this paper, we focus on the influence of the imperfect preparation of the optimal initial probe state to the precision limit of quantum parameter estimation. The analytical results are valid for unitary evolutions with arbitrary dimension.
We study in this work the metrology precision of a probe system coupled to an ancillary qubit. Restricting the probe-qubit coupling along only one or two directions is found to be a sufficient criterion for the effective dynamical generator to achieve the Heisenberg limit in precision. Under the criterion, the quantum Fisher information (QFI) about the to-be-estimated parameter becomes the expectation value of mean square of the effective generator with respect to the initial state of the composite system. Our criterion is justified in two distinct systems. For a bosonic probe, QFI about the displacement estimation is found to be proportional to the mean excitation number of probe. It renders a counterintuitive result that quantum metrology sensitivity can be enhanced by increasing the temperature of the probe system. For a spin-ensemble probe, QFI about both rotation-phase and magnetic-field estimation exhibit a quadratic dependence on the probe-spin number. It is found that even when the spin-ensemble is prepared as a finite-temperature state, faraway from the so-called resource states, e.g., the squeezed state or the Greenberger-Horne-Zeilinger state, QFI can still manifest a Heisenberg scaling behavior.
Abstract In traditional quantum metrology protocols, the initial multipartite entangled pure quantum probes are considered to be isolated, i.e., free of quantum many-body effects. Here, we study the impact of inherent many-body effects such as interaction with noisy environment and nonlocal interactions among particles on metrologically resourceful multipartite entanglement of initially mixed quantum probes. In this regard, we employ an information-theoretic multipartite entanglement measure as a figure-of-merit. The inevitable interaction with the noisy environment leads to disentanglement in multipartite quantum probes which restricts its metrological advantage. For this, we use entanglement dissociation to derive bounds on the multipartite entanglement measure that can identify the relevant entanglement structure under global as well as local noisy evolution. Furthermore, we investigate nonlocal interactions in terms of their entangling capability in a multipartite quantum probe. We show that such nonlocal interactions can be exploited as a valuable resource that exhibits better precision scaling in mixed-state quantum metrology. Moreover, we numerically observe these results for GHZ-W class states.
Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.