Ultimate Precision Limit Research Articles

Achieving the Multiparameter Quantum Cramér-Rao Bound with Antiunitary Symmetry.

The estimation of multiple parameters is a ubiquitous requirement in many quantum metrology applications. However, achieving the ultimate precision limit, i.e., the quantum Cramér-Rao bound, becomes challenging in these scenarios compared to single parameter estimation. To address this issue, optimizing the parameters encoding strategies with the aid of antiunitary symmetry is a novel and comprehensive approach. For demonstration, we propose two types of quantum statistical models exhibiting antiunitary symmetry in experiments. The results showcase the simultaneous achievement of ultimate precision for multiple parameters without any trade-off and the precision is improved at least twice compared to conventional encoding strategies. Our work emphasizes the significant potential of antiunitary symmetry in addressing multiparameter estimation problems.

Quantum enhanced multiple transmission estimation with a bright squeezed light field

Recently, there has been significant interest in multiple-parameter quantum estimation techniques that exploit quantum resources. In particular, the estimation of optical transmission is a crucial parameter in various scientific fields and industries. In optical-based sensing, precision can be enhanced through two approaches: increasing the number of photons that interact with the samples and utilizing quantum states of light. In this paper, we investigate multiple transmission estimation using bright two-mode squeezed states (bTMSSs), which combine the advantages of both bright light and quantum states. We calculate the precision bound for multiple transmission estimation by employing multiple copies of bTMSSs with experimentally feasible optimal measurement, determining both the quantum Cramer-Rao bound and the Cramer-Rao bound. Our results demonstrate that multiple copies of bTMSSs can achieve quantum-enhanced sensitivity for multiple transmissions compared to coherent states, and the ultimate limit of precision can be attained in regions with high nonlinear gain. Furthermore, as an application, we show the quantum-enhanced sensing in circular dichroism sensing using a pair of bTMSSs. Our strategy for multiple transmission estimation offers a practical platform for exploring real-world quantum sensing applications.

Enhanced Quantum Metrology with Non-Phase-Covariant Noise.

The detrimental impact of noise on sensing performance in quantum metrology has been widely recognized by researchers in the field. However, there are no explicit fundamental laws of physics stating that noise invariably weakens quantum metrology. We reveal that phase-covariant noise either degrades or remains neutral to sensing precision, whereas non-phase-covariant noise can potentially enhance parameter estimation, surpassing even the ultimate precision limit achievable in the absence of noise. This implies that a non-Hermitian quantum sensor may outperform its Hermitian counterpart in terms of sensing performance. To illustrate and validate our theory, we present several paradigmatic examples of magnetic field metrology.

Speeding up squeezing with a periodically driven Dicke model

We present a simple and effective method to create highly entangled spin states on a faster timescale than that of the commonly employed one-axis twisting (OAT) model. We demonstrate that by periodically driving the Dicke Hamiltonian at a resonance frequency, the system effectively becomes a two-axis countertwisting Hamiltonian, which is known to quickly create Heisenberg limit scaled entangled states. For these states we show that simple quadrature measurements can saturate the ultimate precision limit for parameter estimation determined by the quantum Cramér-Rao bound. An example experimental realization of the periodically driven scheme is discussed with the potential to quickly generate momentum entanglement in a recently described experimental vertical cavity system. We analyze effects of collective dissipation in this vertical cavity system and find that our squeezing protocol can be more robust than the previous realization of OAT. Published by the American Physical Society 2024

Superresolution imaging of two incoherent optical sources with unequal brightnesses.

Resolving the separation between two incoherent optical sources with high precision is of great significance for fluorescence imaging and astronomical observations. In this paper, we focus on a more general scenario where two sources have unequal brightnesses. We give the ultimate precision limit with respect to separation by using the quantum Fisher information. Through the calculation of the classical Fisher information, we analyze and compare several specific measurement schemes including direct measurement, Gaussian mode measurement and zero-photon measurement. The results indicate that Gaussian mode measurement is the nearly optimal for a small separation. On this basis, the effects of relative brightness fluctuation are addressed. Our work provides a positive complement to the aspect of superresolution imaging of incoherent sources.

Extracting many-body quantum resources within one-body reduced density matrix functional theory

Quantum Fisher information (QFI) is a central concept in quantum sciences used to quantify the ultimate precision limit of parameter estimation, detect quantum phase transitions, witness genuine multipartite entanglement, or probe nonlocality. Despite this widespread range of applications, computing the QFI value of quantum many-body systems is, in general, a very demanding task. Here we combine ideas from functional theories and quantum information to develop a functional framework for the QFI of fermionic and bosonic ground states. By relying upon the constrained-search approach, we demonstrate that the QFI matrix terms can universally be determined by the one-body reduced density matrix (1-RDM), thus avoiding the use of exponentially large wave functions. Furthermore, we show that QFI functionals can be determined from the universal 1-RDM functional by calculating its derivatives with respect to the coupling strengths, thus becoming the generating functional of the QFI. We showcase our approach with the Bose-Hubbard model and present exact analytical and numerical QFI functionals. Our results provide the first connection between the one-body reduced density matrix functional theory and the quantum Fisher information. Published by the American Physical Society 2024

Achieving spatial superresolution with engineered spatial modes

Rayleigh’s criterion sets a limit on the minimum separation between two incoherent point sources to be resolved into distinct objects. However, superresolution techniques have been developed to circumvent Rayleigh’s criterion. These techniques mainly deal with single parameter estimation and require prior information about the centroid. Here, we use multi-parameter estimation tools to simultaneously and optimally retrieve information about the centroid and object separation. Collective measurements on photons using two-photon interference followed by spatially resolved detection have significantly improved over direct detection schemes. Following the same approach, we extend the analysis of the two-photon interference protocol to spatially engineered photons having a Pearson type VII profile with arbitrary positive excess kurtosis. We calculate the precision limits in the current measurement scheme as well as the ultimate precision limits based on the quantum Cramer–Rao bound for different spatial modes. We theoretically show that such engineered pulses show enhanced precision with increasing kurtosis in simultaneous estimation of the centroid and object separation compared to a Gaussian amplitude profile. Furthermore, we discuss an experimental setup to realize the proposed superresolution scheme.

Multiparameter Estimation with Two-Qubit Probes in Noisy Channels.

This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka-Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.

Tilt Measurement at the Quantum Cramer–Rao Bound Using a Higher-Order Hermite–Gaussian Mode

The quantum Cramer–Rao bound (QCRB) provides an ultimate precision limit in parameter estimation. The sensitivity of spatial measurements can be improved by using the higher-order Hermite–Gaussian mode. However, to date, the QCRB-saturating tilt measurement has not been realized. Here, we experimentally demonstrate tilt measurements using a higher-order HG40 mode as the probe beam. Using the balanced homodyne detection with an optimal local beam, which involves the superposition of high-order HG30 and HG50 modes, we demonstrate the precision of the tilt measurement approaching the QCRB. The signal-to-noise ratio of the tilt measurement is enhanced by 9.2 dB compared with the traditional method using HG00 as the probe beam. This scheme is more practical and robust to losses, which has potential applications in areas such as laser interferometer gravitational-wave observatories and high-sensitivity atomic force microscopes.

Cooperation between Coherent Control and Noises in Quantum Metrology

AbstractIn this article, the cooperation between coherent control and noises in open spin systems is studied, aiming to demonstrate that such cooperation can provide new possibilities for parametrization in quantum metrology. The cooperative scheme proposed here outperforms the standard scheme, with higher precision achieved. More specifically, the effect of cooperative interaction between coherent control and noises in conventional single‐spin systems described by Lindblad master equations is illustrated, with the magnitude of a magnetic field taken as the parameter to be estimated and encoded in the noisy dynamics besides the Hamiltonian. The scenarios of both spontaneous emission and dephasing noise have been analyzed, where the associated quantum Fisher information has been given. Furthermore, it has been demonstrated that in the realm where quantum metrology is mostly applied in practice, the precision limit under the cooperative scheme in the presence of noises can surpass the ultimate precision limit under the unitary dynamics. On the other hand, multiple‐spin systems have also been considered. It is shown that the coupling between different spins can help realize non‐local parametrization under the cooperative scheme, with the ground state made entangled. This thus leads to the improvement of precision limit, which has been proved and visualized in this article.

Temporal shaping of wave fields for optimally precise measurements in scattering environments

A wave propagating through a scattering medium typically yields a complex temporal field distribution. Over the years, a number of procedures have emerged to shape the temporal profile of the field in order to temporally focus its energy on a receiver. By analogy, we theoretically and experimentally demonstrate here how to maximize the total Fisher information transmitted to a receiver, and how to focus the Fisher information at any given time. This enables one to estimate the value of any physical observable with optimal precision from noisy measurements, as experimentally illustrated using acoustic waves in the ultrasound regime. By yielding the ultimate precision limit achievable from time-resolved measurements performed in arbitrarily complex media, our approach sets a general benchmark for many applications such as structural health monitoring and biomedical imaging.

Optimal Strategies of Quantum Metrology with a Strict Hierarchy.

One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this Letter, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration. With our framework, we show there exists a strict hierarchy of the precision limits for different families of strategies.

Quantum Fisher information and parameter estimation in non-Hermitian Hamiltonians

Quantum Fisher information bounds the ultimate precision limit in the parameter estimation and has important applications in quantum metrology. In recent years, the theoretical and experimental studies of non-Hermitian Hamiltonians realized in quantum systems have attracted wide attention. Here, the parameter estimation based on eigenstates of non-Hermitian Hamiltonians is investigated, and the corresponding quantum Fisher information and quantum Cramér-Rao bound for the single-parameter and two-parameter estimations are given. In particular, the quantum Fisher information about estimating intrinsic momentum and external parameters in the non-reciprocal and gain-and-loss Su-Schrieffer-Heeger models, and non-Hermitian versions of the quantum Ising chain, Chern-insulator model and two-level system are calculated and analyzed. For these non-Hermitian models, the results show that in the case of single-parameter estimation in these non-Hermitian models, the quantum Fisher information increases significantly in the gapless regime and near the exceptional points, which can improve the accuracy limit of parameter estimation. For the two-parameter estimation, the determinant of the quantum Fisher information matrix also increases obviously near the gapless and exceptional points. In addition, a higher overall accuracy can be achieved in the topological regime than in the trivial regime, and the topological bound in two-parameter estimation can be determined by the Chern number.

Shot-noise-suppressing quantum nonlinearity in the vacuum-field-induced photon-photon interaction

The shot noise in coherent control of a quantum system sets an ultimate precision limit in measurement and information processing. It is caused by the fundamental quantum fluctuation of the photon number of a coherent control field and thus is inevitable. By strongly coupling a two-level system to a quantum vacuum field, we propose an effective $N$-type four-level system. In such a configuration, the coupling of a conventional $N$-type system to a coherent control field is replaced by the quantum vacuum field. As a result, we can achieve a shot-noise-suppressing quantum nonlinearity, due to the vanishing fluctuation of photon number of the quantum vacuum field. The resulting photon blockade effect is only subject to the contribution from the probe field. Thus, it becomes shot-noise suppressing. Our work shows an advantage of a quantum vacuum protocol over a coherent-field protocol in manipulation of quantum systems and presents an opportunity to exploit the quantum vacuum field as a powerful tool in quantum information processing.

Probing cosmic string spacetime through parameter estimation

Quantum metrology studies the ultimate precision limit of physical quantities by using quantum strategy. In this paper we apply the quantum metrology technologies to the relativistic framework for estimating the deficit angle parameter of cosmic string spacetime. We use a two-level atom coupled to electromagnetic fields as the probe and derive its dynamical evolution by treating it as an open quantum system. We estimate the deficit angle parameter by calculating its quantum Fisher information(QFI). It is found that the quantum Fisher information depends on the deficit angle, evolution time, detector initial state, polarization direction, and its position. We then identify the optimal estimation strategies, i.e., maximize the quantum Fisher information via all the associated parameters, and therefore optimize the precision of estimation. Our results show that for different polarization cases the QFIs have different behaviors and different orders of magnitude, which may shed light on the exploration of cosmic string spacetime.

Invariance Property of the Fisher Information in Scattering Media.

Determining the ultimate precision limit for measurements on a subwavelength particle with coherent laser light is a goal with applications in areas as diverse as biophysics and nanotechnology. Here, we demonstrate that surrounding such a particle with a complex scattering environment does, on average, not have any influence on the mean quantum Fisher information associated with measurements on the particle. As a remarkable consequence, the average precision that can be achieved when estimating the particle's properties is the same in the ballistic and in the diffusive scattering regime, independently of the particle's position within its nonabsorbing environment. This invariance law breaks down only in the regime of Anderson localization, due to increased C_{0}-speckle correlations. Finally, we show how these results connect to the mean quantum Fisher information achievable with spatially optimized input fields.

Optimal Scheme for Quantum Metrology

AbstractQuantum metrology can achieve far better precision than classical metrology, and is one of the most important applications of quantum technologies in the real world. To attain the highest precision promised by quantum metrology, all steps of the schemes need to be optimized, which include the state preparation, parametrization, and measurement. Here the recent progresses on the optimization of these steps, which are essential for the identification and achievement of the ultimate precision limit in quantum metrology, are reviewed. It is hoped this provides a useful reference for the researchers in quantum metrology and related fields.

Quantum-Limited Estimation of Range and Velocity

The ultimate precision limits are determined for simultaneously estimating the range and velocity of a target and the range and velocity separations of a pair of targets by using lidar systems, with or without entanglement.

Optimal estimation of gravitation with Kerr nonlinearity in an optomechanical system

We present a high precision scheme of a gravitational accelerometer which consists of an optomechanical system embedding a Kerr nonlinear medium. The quantum Cramer–Rao bound and the quantum Fisher information (QFI) are well-known tools to depict the ultimate precision limit in quantum parameter estimation. In our scheme, the analytical expression of time-dependent QFI is obtained with the absence of noise, which shows that the precision has been improved due to the existence of Kerr nonlinearity. At the light-matter decoupling time, the theoretical bound for the relative sensitivity is $$\varDelta g/g\approx 6.36\times 10^{-13}$$ .

Achieving the ultimate precision limit with a weakly interacting quantum probe

The ultimate precision limit in estimating the Larmor frequency of N unentangled qubits is well established, and is highly important for magnetometers, gyroscopes, and other types of quantum sensors. However, this limit assumes perfect projective measurements of the quantum registers. This requirement is not practical in many physical systems, such as NMR spectroscopy, where a weakly interacting external probe is used as a measurement device. Here, we show that in the framework of quantum nano-NMR spectroscopy, in which these limitations are inherent, the ultimate precision limit is still achievable using control and a finely tuned measurement.