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In this expository paper, we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and Z X -calculus, establishing a connection between quantum computing questions and quantum groups, i.e. Hopf algebras. [ABSTRACT FROM AUTHOR]

The article is part of a course on Quantum Information Technologies QIT conducted at the Faculty of Electronics and Information Technology of the Warsaw University of Technology. The subject includes a publishing workshop exercised by engineering students. How do ICT engineers see QIT from their point of view? How can they implement quantum technologies in their future work? M.Sc. students usually have strictly declared topics for their master’s theses. The implementation of some works is at an advanced stage. The potential areas of application of QIT are defined and narrow if they are to intellectually expand the area of the completed theses. This is the idea of incorporating QIT components or interfaces into classic ICT solutions at the software and hardware level. It is possible to propose a solution in the form of a functional hybrid system. QIT systems should be functionally incorporated into the existing ICT environment, generating measurable added value. Such a task is quite demanding, but practice shows that it interests students. Solutions don’t have to be mature or even feasible. They can be dreams of young engineers. The exercise is a publication workshop related to the fast development of QIT. The article is a continuation of publication exercises conducted with previous groups of students participating in QIT lectures.

Atomic nonlinear interferometry has wide applications in quantum metrology and quantum information science. Here we propose a nonlinear time-reversal interferometry scheme with high robustness and metrological gain based on the spin squeezing generated by arbitrary quadratic collective-spin interaction, which could be described by the Lipkin–Meshkov–Glick (LMG) model. We optimize the squeezing process, encoding process, and anti-squeezing process, finding that the two particular cases of the LMG model, one-axis twisting and two-axis twisting outperform in robustness and precision, respectively. Moreover, we propose a Floquet driving method to realize equivalent time reverse in the atomic system, which leads to high performance in precision, robustness, and operability. Our study sets a benchmark for achieving high precision and high robustness in atomic nonlinear interferometry. [ABSTRACT FROM AUTHOR]

We investigate the utilization of advanced single photons produced by quantum dots (QDs) in a microcavity for quantum metrology. Through the integration of lateral excitation and the Purcell effect in an Fabry–Perot microcavity, we realized single-photon emission with an extraction efficiency of 46.39%, high purity of 96.91%, and high indistinguishability of 98.32%. Our QD-generated single photons enabled the creation of high-quality NOON states (N = 2) for phase measurement, yielding an interference contrast of 79.79% and surpassing the standard quantum limit (SQL) with phase super-sensitivity. Our results underscore the immense potential of QD-derived single photons for propelling quantum metrology forward, facilitating enhanced precision measurements across diverse applications. [ABSTRACT FROM AUTHOR]

A quantum metrology problem of simultaneous measurement and estimation of several phase parameters was considered in the framework of current tendencies of development of alternative navigation. The fundamental limits of both linear and nonlinear metrology were studied. The effect of losses on the accuracy of quantum metrology of several phase parameters was analyzed. A method to prepare three-mode N00N- states using atomic bright solitons was proposed. [ABSTRACT FROM AUTHOR]

The most direct approach for characterizing the quantum dynamics of a strongly interacting system is to measure the time evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate approach is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Here we investigate what the decoherence dynamics of such a probe tells us about the many-body system. In particular, we utilize optically addressable probe spins to experimentally characterize both static and dynamical properties of strongly interacting magnetic dipoles. Our experimental platform consists of two types of spin defects in nitrogen delta-doped diamond: nitrogen-vacancy colour centres, which we use as probe spins, and a many-body ensemble of substitutional nitrogen impurities. We demonstrate that the many-body system's dimensionality, dynamics and disorder are naturally encoded in the probe spins' decoherence profile. Furthermore, we obtain direct control over the spectral properties of the many-body system, with potential applications in quantum sensing and simulation.

Evaluating quantum Fisher information is an essential task in the parameter estimation and quantum metrology. It quantifies the sensitivity of a quantum state to probe and capture variations in an unknown parameter, which is aimed to be estimated. In this context, the amount of quantum Fisher information measures the operational nonclassicality of a given state, regarded as a quantifiable resource for quantum metrology. We construct su(1, 1) coherent states, using the Perelomov formalism, and present their various optical realizations forming a general class of su(1, 1) algebraic squeezed states. We analyze the nonclassicality of these states and evaluate the corresponding Fisher information. Also, we find that su(1, 1) algebraic squeezed states surpass the standard quantum limit, thereby exhibiting a quantum metrological advantage. [ABSTRACT FROM AUTHOR]

The article is part of a course on Quantum Information Technologies QIT conducted at the Faculty of Electronics and Information Technology of the Warsaw University of Technology. The subject includes a publishing workshop exercised by engineering students. How do ICT engineers see QIT from their point of view? How can they implement quantum technologies in their future work? M.Sc. students usually have strictly declared topics for their master's theses. The implementation of some works is at an advanced stage. The potential areas of application of QIT are defined and narrow if they are to intellectually expand the area of the completed theses. This is the idea of incorporating QIT components or interfaces into classic ICT solutions at the software and hardware level. It is possible to propose a solution in the form of a functional hybrid system. QIT systems should be functionally incorporated into the existing ICT environment, generating measurable added value. Such a task is quite demanding, but practice shows that it interests students. Solutions don't have to be mature or even feasible. They can be dreams of young engineers. The exercise is a publication workshop related to the fast development of QIT. The article is a continuation of publication exercises conducted with previous groups of students participating in QIT lectures. [ABSTRACT FROM AUTHOR]

Parity or quadratic spin (e.g., J2z) readouts of a Mach-Zehnder (MZ) interferometer probed with a twin Fock (TF) input state allow saturating the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles but only when the interferometer phase θ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at θ = 0, whereas better-than-standard quantum limit performance of the J2z readout is restricted to an o(√N) occupation imbalance. We show that a method of moments readout of two quadratic spin observables J2z and J2+ + J2- is globally optimal for Dicke state probes; i.e., the error saturates the QFI for all θ. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on TF states, showing that the method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of θ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four-mode state |N/4, N/4, N/4, N/4〉 and its lossy counterparts, showing that an advantage for the estimation of any linear function of the local MZ phases θ1 and θ2 (compared to independent probing of the MZ phases by two copies of |N/4, N/4〉) appears when more than one particle is lost. [ABSTRACT FROM AUTHOR]

Quantum metrology, such as quantum phase estimation, can surpass classical sensing limits, reaching the Heisenberg‐scaling precision. So far, this kind of metrology has been thought to be only implementable with the quantum systems, which, however, are fragile to environmental noise and hardly contribute to the practical detections. Herein, it is demonstrated both theoretically and experimentally that the parameter encoded by the optical phase can also be estimated at the Heisenberg scaling in classical optics. Inspired by the quantum‐entanglement‐enhanced sensing scheme, the estimation is performed by using classically correlated beams as probes, and obtaining the probes readout after their interaction with the target system. Because the correlated beams considered are spatially separable, a distributed phase estimation scheme is given, which can sense the linear combinations of the phase shifts induced by distinct systems. The results of our experiments show an error reduction up to 3.89 dB below the classical limit when the correlated beam number for probing is 6, approaching the Heisenberg limit. Compared with quantum strategies, the proposal shows a better robustness against the environmental disturbance and keeps their performances even when the correlated beam number is relatively large. Hence, it indicates promising practical applications in the future. [ABSTRACT FROM AUTHOR]

Abstract The detection of weak time-dependent alternating signals in a strongly noisy background is an important problem in physics and a critical task in metrology. Quantum lock-in amplifier can extract alternating signals within extreme noises by using suitable quantum resources, which has been widely used for magnetic field sensing, vector light shift detection, and force detection. In particular, entanglement-enhanced quantum lock-in amplifier can be realized via many-body quantum interferometry. The many-body lock-in measurement provides a feasible way to achieve high-precision detection of alternating signals, even in noisy environments. In this article, we review general protocol, experiment progresses and potential applications of quantum lock-in measurements.

The detection of weak time-dependent alternating signals in a strongly noisy background is an important problem in physics and a critical task in metrology. Quantum lock-in amplifier can extract alternating signals within extreme noises by using suitable quantum resources, which has been widely used for magnetic field sensing, vector light shift detection, and force detection. In particular, entanglement-enhanced quantum lock-in amplifier can be realized via many-body quantum interferometry. The many-body lock-in measurement provides a feasible way to achieve high-precision detection of alternating signals, even in noisy environments. In this article, we review general protocol, experiment progresses and potential applications of quantum lock-in measurements. [ABSTRACT FROM AUTHOR]

The recent advances in Machine Learning hold great promises for the field of quantum sensing and metrology. With the help of reinforcement learning, we can tame the complexity of quantum systems and solve the problem of optimal experimental design. Reinforcement learning is a powerful model-free technique that allows an agent, which is typically a neural network, to learn the best strategy to reach a certain goal in a completely a priori unknown environment. However, in general, we know something about the quantum system the agent is interacting with, at least that it follows the rules of quantum mechanics. In quantum metrology, we typically have a model for the system and only some parameters of the evolution or of the initial state are unknown. We present here a general Machine Learning technique that can optimize the precision of quantum sensors, and in doing so it exploits the knowledge we have on the system. We have developed a Python package to automate a broad class of optimizations that can be found in the tasks of quantum parameter estimation, quantum metrology and quantum hypothesis testing. What the agent is learning here is an optimal adaptive strategy, that, on the basis of the previous outcomes, decides the next measurements to perform. It works both for Bayesian estimation and for frequentist estimation. The user is required to implement the physics of the system to be studied and state which parameters in the experiment are controllable and which are unknowns. The functions of the library allow then to easily train a neural network agent for optimizing the precision of the sensor, by simulating the experiment. We have explored some applications of this technique to magnetometry on NV centers (both DC and AC), to state discrimination in quantum optics and to phase estimation. So far, we were able to certify better results than the current state-of-the-art controls for many examples. The Machine Learning technique developed here can be applied in all those scenarios where the quantum system is well characterized and relatively simple and small. In these cases, we can squeeze every last bit of information from a quantum sensor by controlling it with a neural network appropriately trained. [ABSTRACT FROM AUTHOR]

A ghost spectroscopy measurement with an entangled photon source is demonstrated. The transmission spectrum at the 2 μ$\umu$m absorption peak of gaseous carbon dioxide (CO2) is measured in a highly noisy environment. Despite the noise, a high sensitivity S=(5.7±0.1)×10−2$S = (5.7\pm 0.1)\times 10^{-2}$(g/l)−1$\mathrm{(g/l)^{-1}}$ is obtained, a value that is larger than the one found for a classical spectroscopy measurement performed in the same conditions. The probe photons are time‐energy correlated photon pairs generated through intermodal spontaneous four‐wave mixing in a silicon waveguide. This observation opens the way to low‐cost on‐chip MIR sensors insensitive to environmental noise. [ABSTRACT FROM AUTHOR]

Parity or quadratic spin (e.g., Jz2) readouts of a Mach–Zehnder (MZ) interferometer probed with a twin Fock (TF) input state allow saturating the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles but only when the interferometer phase θ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at θ = 0, whereas better-than-standard quantum limit performance of the Jz2 readout is restricted to an o(N) occupation imbalance. We show that a method of moments readout of two quadratic spin observables Jz2 and J+2+J−2 is globally optimal for Dicke state probes; i.e., the error saturates the QFI for all θ. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on TF states, showing that the method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of θ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four-mode state |N4,N4,N4,N4〉 and its lossy counterparts, showing that an advantage for the estimation of any linear function of the local MZ phases θ1 and θ2 (compared to independent probing of the MZ phases by two copies of |N4,N4〉) appears when more than one particle is lost.

Quantum metrology, such as quantum phase estimation, can surpass classical sensing limits, reaching the Heisenberg‐scaling precision. So far, this kind of metrology has been thought to be only implementable with the quantum systems, which, however, are fragile to environmental noise and hardly contribute to the practical detections. Herein, it is demonstrated both theoretically and experimentally that the parameter encoded by the optical phase can also be estimated at the Heisenberg scaling in classical optics. Inspired by the quantum‐entanglement‐enhanced sensing scheme, the estimation is performed by using classically correlated beams as probes, and obtaining the probes readout after their interaction with the target system. Because the correlated beams considered are spatially separable, a distributed phase estimation scheme is given, which can sense the linear combinations of the phase shifts induced by distinct systems. The results of our experiments show an error reduction up to 3.89 dB below the classical limit when the correlated beam number for probing is 6, approaching the Heisenberg limit. Compared with quantum strategies, the proposal shows a better robustness against the environmental disturbance and keeps their performances even when the correlated beam number is relatively large. Hence, it indicates promising practical applications in the future.

Abstract Quantum metrology aims at delivering new quantum-mechanical improvement to technologies of parameter estimations with precision bounded by the quantum Cramér-Rao bound. The currently used quantum Cramér-Rao bound was established with measurements of observables restricted to be Hermitian. This constrains the bound and limits the precision of parameter estimation. In this paper, we lift the constraint and derive a previously unknown quantum Cramér-Rao bound. We find that the new bound can reach arbitrary small value with mixed states and it breaks the Heisenberg limit in some cases. We construct a setup to measure non-Hermitian operators and discuss the saturation of the present bound. Two examples—the phase estimation with Greenberger-Horne-Zeilinger states of trapped ions and the adiabatic quantum parameter estimation with the nuclear magnetic resonance—are employed to demonstrate the theory. The present study might open a new research direction—non-Hermitian quantum metrology.

We study the phase sensitivity of a Mach–Zehnder interferometer (MZI) with product detection (PD) scheme by using the superposition of Schrödinger’s cat-like state with the vacuum state (SCVS) and the coherent state as the inputs. We compare the results derived from PD with the parity detection scheme’s results. We found that PD performs better than parity detection and approaches the single parameter quantum Cramér-Rao bound in some cases. Therefore, we expect that SCVS may play as an alternative quantum resource with PD for the improvement in the phase sensitivity of an MZI having potential application in quantum metrology and quantum sensing.

Quantum metrology aims at delivering new quantum-mechanical improvement to technologies of parameter estimations with precision bounded by the quantum Cramér-Rao bound. The currently used quantum Cramér-Rao bound was established with measurements of observables restricted to be Hermitian. This constrains the bound and limits the precision of parameter estimation. In this paper, we lift the constraint and derive a previously unknown quantum Cramér-Rao bound. We find that the new bound can reach arbitrary small value with mixed states and it breaks the Heisenberg limit in some cases. We construct a setup to measure non-Hermitian operators and discuss the saturation of the present bound. Two examples—the phase estimation with Greenberger-Horne-Zeilinger states of trapped ions and the adiabatic quantum parameter estimation with the nuclear magnetic resonance—are employed to demonstrate the theory. The present study might open a new research direction—non-Hermitian quantum metrology. [ABSTRACT FROM AUTHOR]

Quantum Fisher information matrix (QFIM) is a fundamental quantity in quantum physics, which closely links to diverse fields such as quantum metrology, phase transitions, entanglement witness, and quantum speed limit. It is crucial in quantum parameter estimation, central to the ultimate Cramér-Rao bound. Recently, the evaluation of QFIM using quantum circuit algorithms has been proposed for systems with multiplicative parameters Hamiltonian. However, systems with generic Hamiltonians still lack these proposed schemes. This work introduces a quantum-circuit-based approach for evaluating QFIM with generic Hamiltonians. We present a time-dependent stochastic parameter-shift rule for the derivatives of evolved quantum states, whereby the QFIM can be obtained. The scheme can be executed in universal quantum computers under the family of parameterized gates. In magnetic field estimations, we demonstrate the consistency between the results obtained from the stochastic parameter-shift rule and the exact results, while the results obtained from a standard parameter-shift rule slightly deviate from the exact ones. Our work sheds new light on studying QFIM with generic Hamiltonians using quantum circuit algorithms. [ABSTRACT FROM AUTHOR]

We investigate the utilization of advanced single photons produced by quantum dots (QDs) in a microcavity for quantum metrology. Through the integration of lateral excitation and the Purcell effect in an Fabry–Perot microcavity, we realized single-photon emission with an extraction efficiency of 46.39%, high purity of 96.91%, and high indistinguishability of 98.32%. Our QD-generated single photons enabled the creation of high-quality NOON states (N = 2) for phase measurement, yielding an interference contrast of 79.79% and surpassing the standard quantum limit (SQL) with phase super-sensitivity. Our results underscore the immense potential of QD-derived single photons for propelling quantum metrology forward, facilitating enhanced precision measurements across diverse applications.

The article explores the field of quantum sensing and metrology, which allows for highly sensitive measurements of various factors. Quantum sensors can observe information at the nanometer scale, but further advancements are needed in materials and control methods. The article highlights the potential of quantum sensing and metrology in various fields. It also discusses a study on the creation of position-controlled color centers in a silicon carbide pn junction diode, which has implications for quantum science and technology. [Extracted from the article]

While the quantum metrological advantages of performing non‐Gaussian operations on two‐mode squeezed vacuum (TMSV) states have been extensively explored, similar studies in the context of two‐mode squeezed thermal (TMST) states are severely lacking. This paper explores the potential advantages of performing non‐Gaussian operations on TMST state for phase estimation using parity detection‐based Mach–Zehnder interferometry and compares it with the TMSV case. To this end, a realistic photon subtraction, addition, and catalysis model is considered. A unified Wigner function of the photon subtracted, photon added, and photon catalyzed TMST state is derived, which is used to obtain the expression for the phase sensitivity. The results show that performing non‐Gaussian operations on TMST states can enhance the phase sensitivity for significant squeezing and transmissivity parameter ranges. Because of the probabilistic nature of these operations, it is of utmost importance to consider their success probability. When the success probability is considered, the photon catalysis operation performed using a high transmissivity beam splitter is the optimal non‐Gaussian operation. This contrasts with the TMSV case, where photon addition is observed as the most optimal. Further, the derived Wigner function of the non‐Gaussian TMST states will be useful for state characterization and various quantum protocols. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We propose a method to generate the multi-mode entangled catalysis squeezed vacuum states (MECSVS) by embedding the cross-Kerr nonlinear medium into the Mach—Zehnder interferometer. This method realizes the exchange of quantum states between different modes based on Fredkin gate. In addition, we study the MECSVS as the probe state of multi-arm optical interferometer to realize multi-phase simultaneous estimation. The results show that the quantum Cramer—Rao bound (QCRB) of phase estimation can be improved by increasing the number of catalytic photons or decreasing the transmissivity of the optical beam splitter using for photon catalysis. In addition, we also show that even if there is photon loss, the QCRB of our photon catalysis scheme is lower than that of the ideal entangled squeezed vacuum states (ESVS), which shows that by performing the photon catalytic operation is more robust against photon loss than that without the catalytic operation. The results here can find applications in quantum metrology for multiparatmeter estimation. [ABSTRACT FROM AUTHOR]

High-sensitivity interferometers are one of the basic tools for precision measurement, and their sensitivity is limited by their shot noise limit (SNL), which is determined by vacuum fluctuations of the probe field. The quantum interferometer with novel structures can break the SNL and measure the weak signals, such as the direct observation of gravity wave signal. Combining classical interferometers and the optical parametric amplifier (OPA) can enhance the signal; meanwhile, the quantum noise is kept at the vacuum level, so that the sensitivity of the nonlinear interferometer beyond the SNL can be achieved. By analyzing in detail the influence of system parameters on the precision of quantum metrology, including the intensity of optical fields for phase sensing, the gain factor of OPA, and the losses inside and outside the interferometers, the application conditions of high-sensitivity nonlinear quantum interferometers are obtained. Quantum interferometer-based OPAs provide the direct references for the practical development of quantum precise measurement. [ABSTRACT FROM AUTHOR]

A new time‐domain method for subcycle metrology of quantum electric fields using a combination of a third order nonlinear optical process and homodyne detection with a local oscillator (LO) field is proposed and analyzed. The new method enables isolation of intrinsically weak quantum noise contribution by subtraction of the shot noise of the LO on a pulse‐by‐pulse basis. Together with the centro‐symmetric character of the nonlinearity, this method unlocks novel opportunities toward terahertz and mid‐infrared quantum field metrologies. [ABSTRACT FROM AUTHOR]

We study the improvement in the phase sensitivity of a Mach–Zehnder interferometer (MZI) using the superposition of 'Schrödinger's cat-like state with the vacuum state (SCVS)' and the vacuum state as inputs. With this setup, we examine the effect on the phase sensitivity of the interferometer using a parity detection scheme. We find better phase sensitivity under some conditions for this setup having potential application in quantum sensing. [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

Frequency up-conversion has become amongst the most prevalent techniques for detection of terahertz waves in metrology systems. State-of-the-art upconversion techniques rely on the coherent transferring of the information encoded in all degrees of freedom of a terahertz wave to either the nearinfrared or visible domain, where detectors are readily accessible. This allows for an indirect reconstruction of the terahertz wave. However, unlike most upconversion methods employed in photonics which are concentrating on narrowband tones (at both terahertz and near-infrared frequencies), a broadband, hence temporally constrained, terahertz transient is sampled on time-scales shorter than its oscillation period. Here, femtosecond laser pules serve as temporal gates. In this perspective, we highlight several hallmarks of terahertz metrology that originate from these sub-cycle measurement capabilities and elaborate why this enables studies in fundamental and applied science, with a particular focus on novel measurement concepts in classical and quantum. We focus on so-far demonstrated detection performance in bulk non-linear crystals. Finally, we discuss current challenges and the most pressing questions ahead. [ABSTRACT FROM AUTHOR]

Time and frequency (T&F) measurement with unprecedented accuracy is the backbone for several sophisticated technologies, commensurate with the evolution of human civilisation in the 20th century in terms of communication, positioning, navigation, and precision timing. This necessity drove researchers in the early 1950s to build atomic clocks that have now evolved to a state-of-the-art level, operating at optical wavelengths as optical atomic clocks, which use cold and trapped samples of atomic/ionic species and various other sophisticated diagnostic test techniques. Such ultrahigh-precision accurate clocks have made it possible to probe fundamental aspects of science through incredibly sensitive measurements. On the other hand, they meet the T&F synchronisation standards for classical and emerging quantum technologies at the desired level of accuracy. Considering the impact of optical atomic clocks in the second quantum revolution (quantum 2.0), they have been identified as an indispensable critical technology in worldwide quantum missions, including in India. This article reviews the present international scenario regarding optical atomic clocks and their related technologies and draws a roadmap for their indigenisation over the next decade. [ABSTRACT FROM AUTHOR]

We make use of the powerful formalism of quantum parameter estimation to assess the characteristic rates of a continuous spontaneous localization (CSL) model affecting the motion of a massive mechanical system. We show that a study performed in non-equilibrium conditions unveils the advantages provided by the use of genuinely quantum resources—such as quantum correlations—in estimating the CSL-induced diffusion rate. In stationary conditions, instead, the gap between quantum performance and a classical scheme disappears. Our investigation contributes to the ongoing effort aimed at identifying suitable conditions for the experimental assessment of collapse models. [ABSTRACT FROM AUTHOR]

The quantum version of a special classical Wheatstone bridge built with a boundary-driven spin system has recently been proposed. We propose a quantum Wheatstone bridge consisting of Bose systems, which can simulate the general classical Wheatstone bridge. Unknown coupling can be obtained when the quantum Wheatstone bridge is balanced, which can be determined simply by homodyne detection. When the expectation value of the homodyne detection is 0, the quantum Wheatstone bridge is unbalanced. When the expectation value of the homodyne detection is proportional to the square root of the initial number of bosons by regulating a known coupling strength, the quantum Wheatstone bridge is balanced. By calculating the quantum Fisher information, we show that the measurement precision is optimal when the quantum Wheatstone bridge is balanced. And the homodyne detection is close to the optimal measurement in the case of low-temperature baths.

Classical polarimetry is a well-established discipline with diverse applications across different branches of science. The burgeoning interest in leveraging quantum resources to achieve highly sensitive measurements has spurred researchers to elucidate the behavior of polarized light within a quantum mechanical framework, thereby fostering the development of a quantum theory of polarimetry. In this work, drawing inspiration from polarimetric investigations in biological tissues, we investigate the precision limits of polarization rotation angle estimation about a known rotation axis, in a quantum polarimetric process, comprising three distinct quantum channels. The rotation angle to be estimated is induced by the retarder channel on the Stokes vector of the probe state. The diattenuator and depolarizer channels, acting on the probe state, can be thought of as effective noise processes. We explore the precision constraints inherent in quantum polarimetry by evaluating the quantum Fisher information for probe states of significance in quantum metrology, namely NOON, Kings of Quantumness, and Coherent states. The effects of the noise channels as well as their ordering is analyzed on the estimation error of the rotation angle to characterize practical and optimal quantum probe states for quantum polarimetry. Furthermore, we propose an experimental framework tailored for NOON state quantum polarimetry, aiming to bridge theoretical insights with empirical validation.

Multi-mode NOON states can quantum-enhance multiple-phase estimation in the absence of photon loss. However, a multi-mode NOON state is known to be vulnerable to photon loss, and its quantum-enhancement can be dissipated by lossy environment. In this work, we demonstrate that a quantum advantage in estimate precision can still be achieved in the presence of photon loss. This is accomplished by optimizing the weights of the multi-mode NOON states according to photon loss rates in the multiple modes, including the reference mode which defines the other phases. For practical relevance, we also show that photon-number counting via a multi-mode beam-splitter achieves the useful, albeit sub-optimal, quantum advantage. We expect this work to provide valuable guidance for developing quantum-enhanced multiple-phase estimation techniques in lossy environments.

Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply our results to the estimation of the transverse displacement of a beam and to the temporal separation between two pulses. For these examples, we show how the estimation sensitivity can be enhanced by adding squeezing into specific modes.

Accurate phase estimation in the presence of unknown phase diffusive noise is a crucial yet challenging task in noisy quantum metrology. This problem is particularly interesting due to the detrimental impact of the associated noise. Here, we investigate the joint estimation of phase and phase diffusion using generalized Holland–Burnett states, known for their experimental accessibility. These states provide performance close to the optimal state in single-parameter phase estimation, even in the presence of photon losses. We adopt a twofold approach by analyzing the joint information extraction through the double homodyne measurement and the joint information availability across all probe states. Through our analysis, we find that the highest sensitivities are obtained by using states created by directing all input photons into one port of a balanced beam splitter. Furthermore, we infer that good levels of sensitivity persist even in the presence of moderate photon losses, illustrating the remarkable resilience of our probe states under lossy conditions.

We address quantum characterization of anisotropic spin chains in the presence of anti-symmetric exchange, and investigate whether the Hamiltonian parameters of the chain may be estimated with precision approaching the ultimate limit imposed by quantum mechanics. At variance with previous approaches, we focus on the information that may be extracted by measuring only two neighboring spins rather than a global observable on the entire chain. We evaluate the Fisher information (FI) of a two-spin magnetization measure, and the corresponding quantum Fisher information (QFI), for all the relevant parameters, i.e. the spin coupling, the anisotropy, and the Dzyaloshinskii–Moriya (DM) parameter. Our results show that the reduced system made of two neighboring spins may be indeed exploited as a probe to characterize global properties of the entire system. In particular, we find that the ratio between the FI and the QFI is close to unit for a large range of the coupling values. The DM coupling is beneficial for coupling estimation, since it leads to the presence of additional bumps and peaks in the FI and QFI, which are not present in a model that neglects exchange interaction and may be exploited to increase the robustness of the overall estimation procedure. Finally, we address the multiparameter estimation problem, and show that the model is compatible but sloppy, i.e. both the Uhlmann curvature and the determinant of the QFI matrix vanish. Physically, this means that the state of the system actually depends only on a reduced numbers of combinations of parameters, and not on all of them separately.

We provide new operational significance of nonclassicality in nonequilibrium temperature estimation of bosonic baths with Gaussian probe states and Gaussian dynamics. We find a bound on the thermometry performance using classical probe states. Then we show that by using nonclassical probe states, single-mode and two-mode squeezed vacuum states, one can profoundly improve the classical limit. Interestingly, we observe that this improvement can also be achieved by using Gaussian measurements. Hence, we propose a fully Gaussian protocol for enhanced thermometry, which can simply be realized and used in quantum optics platforms.

We consider quantum metrology with several copies of bipartite and multipartite quantum states. We characterize the metrological usefulness by determining how much the state outperforms separable states. We identify a large class of entangled states that become maximally useful for metrology in the limit of large number of copies, even if the state is weakly entangled and not even more useful than separable states. This way we activate metrologically useful genuine multipartite entanglement. Remarkably, not only that the maximally achievable metrological usefulness is attained exponentially fast in the number of copies, but it can be achieved by the measurement of few simple correlation observables. We also make general statements about the usefulness of a single copy of pure entangled states. We surprisingly find that the multiqubit states presented in Hyllus et al (2010 Phys. Rev. A 82 012337), which are not useful, become useful if we embed the qubits locally in qutrits. We discuss the relation of our scheme to error correction, and its possible use for quantum metrology in a noisy environment.

Quantum sensing using non-linear interferometers (NLIs) offers the possibility of bicolour imaging, using light that never interacted with the object of interest, and provides a way to achieve phase supersensitivity, i.e. a Heisenberg-type scaling of the phase uncertainty. Such a scaling behaviour is extremely susceptible to noise and only arises at specific phases that define the optimal working point (WP) of the device. While phase-shifting algorithms are to some degree robust against the deleterious effects induced by noise they extract an image by tuning the interferometer phase over a broad range, implying an operation beyond the WP. In our theoretical study, we investigate both the spontaneous and the high-gain regime of operation of an NLI. In fact, in the spontaneous regime using a distillation technique and operating at the WP leads to a qualitatively similar behaviour. In the high-gain regime, however, typical distillation techniques inherently forbid a scaling better than the standard-quantum limit, as a consequence of the photon statistics of squeezed vacuum. In contrast, an operation at the WP still may lead to a sensitivity below shot noise, even in the presence of noise. Therefore, this procedure opens the perspective of bicolour imaging with a better than shot-noise phase uncertainty by working in the vicinity of the WP. Our results transfer quantum imaging distillation in a noisy environment to the high-gain regime with the ultimate goal of harnessing its full potential by combining bicolour imaging and phase supersensitivity.

We characterise the measurement sensitivity, quantified by the quantum Fisher information (QFI), of a single-fermionic thermometric probe strongly coupled to the sample of interest, a fermionic bath, at temperature T . For nonequilibrium protocols, in which the probe is measured before reaching equilibrium with the sample, we find new behaviour of the measurement sensitivity arising due to non-Markovian dynamics. First, we show that the QFI displays a highly non-monotonic behaviour in time, in contrast to the Markovian case where it grows monotonically until equilibrium, so that non-Markovian revivals can be exploited to reach a higher QFI. Second, the QFI rate is maximised at a finite interrogation time $t^*$ , which we characterize, in contrast to the solution $t^* \rightarrow 0$ known in the Markovian limit (Pavel Sekatski and Martí Perarnau-Llobet 2022 Quantum 6 869). Finally, we consider probes make up of few fermions and discuss different collective enhancements in the measurement precision.

We show that the lowest quantum Cramér-Rao bound achievable in interferometry with a one-axis twisted spin coherent state is saturated by the asymptotic method of moments error of a protocol that uses one call to the one-axis twisting, one call to time-reversed one-axis twisting, and a final total spin measurement (i.e., a twist-untwist protocol). The result is derived by first showing that the metrological phase diagram for one-axis twisting is asymptotically characterized by a single quantum Fisher information value N ( N + 1)/2 for all times, then constructing a twist-untwist protocol having a method of moments error that saturates this value. The case of finite-range one-axis twisting is similarly analyzed, and a simple functional form for the metrological phase diagram is found in both the short-range and long-range interaction regimes. Numerical evidence suggests that the finite-range analogues of twist-untwist protocols can exhibit a method of moments error that asymptotically saturates the lowest quantum Cramér-Rao bound achievable in interferometry with finite-range one-axis twisted spin coherent states for all interaction times.

The deterioration of precision caused by quantum decoherence in dissipative environments is a longstanding problem in the development of quantum metrology. Therefore, it is significant to effectively analyze the evolution of quantum systems under dissipative environments and quantitatively estimate the parameters given a certain probe. Here, we propose a continuous-variable (CV) quantum metrology scheme within the Bayesian paradigm to estimate phase shift, loss coefficient and temperature of a dissipative environment. Through numerical evaluation and concrete analysis, we investigate the achievable precision of Bayesian quantum parameter estimation with Gaussian states and homodyne measurements, and the influence of different parameters on the estimation process. More interestingly, the scheme can be applied in more practical scenarios where not enough measurements are obtained and the frequentist analysis is not well defined.

In this paper, we consider the application of quantum reservoir engineering in quantum metrology. More precisely, we are concerned with a system setup where a sequence of atoms constructing the "time-varying" quantum reservoir interact, in turn, with the trapped field in a cavity through the Jaynes–Cummings Hamiltonian. In particular, we were able to manipulate the initial states of reservoir atoms in order to enhance estimation precision regarding the coupling strength between each atom and the cavity (the coupling strength between each atom and the cavity was assumed to be identical). The novelty of this work lies in alternately preparing the atoms at two different states in a pairwise manner, such that the cavity could converge into a squeezed state with photonic loss to the environment taken into account. The control scheme proposed here thus leads to higher precision compared to the previous work where reservoir atoms were initialized at the same state, which drove the cavity to a coherent state. Detailed theoretical analysis and numerical simulations are also provided. In addition, this system setup and the associated control scheme are easily implemented for quantum metrology, since no entanglement is required for the preparation of atom states, and the final cavity state can stay steady. [ABSTRACT FROM AUTHOR]

The Wigner D-matrix is essential in the course of angular momentum techniques. We here derive the new even- and odd-orthogonality properties of the Wigner D-matrix which was yet to be demonstrated in textbooks and also apply them to identifying optimal measurements for linear phase estimation based on two-mode optical interferometry with two specific quantum states. [ABSTRACT FROM AUTHOR]