Multiparameter squeezing for optimal quantum enhancements in sensor networks

Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics

Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.

Exploiting Nonclassical Motion of a Trapped Ion Crystal for Quantum-Enhanced Metrology of Global and Differential Spin Rotations

We theoretically investigate prospects for the creation of nonclassical spin states in trapped ion arrays by coupling to a squeezed state of the collective motion of the ions. The correlations of the generated spin states can be tailored for quantum-enhanced sensing of global or differential rotations of subensembles of the spins by working with specific vibrational modes of the ion array. We propose a pair of protocols to utilize the generated states and demonstrate their viability even for small systems, while assessing limitations imposed by spin-motion entanglement and technical noise. Our work suggests new opportunities for the preparation of many-body states with tailored correlations for quantum-enhanced metrology in spin-boson systems.

Quantum Precision Limits of Displacement Noise-Free Interferometers

Current laser-interferometric gravitational wave detectors suffer from a fundamental limit to their precision due to the displacement noise of optical elements contributed by various sources. Several schemes for displacement noise-free interferometers (DFI) have been proposed to mitigate their effects. The idea behind these schemes is similar to decoherence-free subspaces in quantum sensing; i.e., certain modes contain information about the gravitational waves but are insensitive to the mirror motion (displacement noise). We derive quantum precision limits for general DFI schemes, including optimal measurement basis and optimal squeezing schemes. We introduce a triangular cavity DFI scheme and apply our general bounds to it. Precision analysis of this scheme with different noise models shows that the DFI property leads to interesting sensitivity profiles and improved precision due to noise mitigation and larger gain from squeezing.

Distributed quantum sensing of multiple phases with fewer photons

Distributed quantum metrology has drawn intense interest as it outperforms the optimal classical counterparts in estimating multiple distributed parameters. However, most schemes so far have required entangled resources consisting of photon numbers equal to or more than the parameter numbers, which is a fairly demanding requirement as the number of nodes increases. Here, we present a distributed quantum sensing scenario in which quantum-enhanced sensitivity can be achieved with fewer photons than the number of parameters. As an experimental demonstration, using a two-photon entangled state, we estimate four phases distributed 3 km away from the central node, resulting in a 2.2 dB sensitivity enhancement from the standard quantum limit. Our results show that the Heisenberg scaling can be achieved even when using fewer photons than the number of parameters. We believe our scheme will open a pathway to perform large-scale distributed quantum sensing with currently available entangled sources.

Variational quantum metrology for multiparameter estimation under dephasing noise

We present a hybrid quantum-classical variational scheme to enhance precision in quantum metrology. In the scheme, both the initial state and the measurement basis in the quantum part are parameterized and optimized via the classical part. It enables the maximization of information gained about the measured quantity. We discuss specific applications to 3D magnetic field sensing under several dephasing noise models. Indeed, we demonstrate its ability to simultaneously estimate all parameters and surpass the standard quantum limit, making it a powerful tool for metrological applications.

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.

Distributed quantum sensing with mode-entangled spin-squeezed atomic states

Quantum sensors are used for precision timekeeping, field sensing and quantum communication^1-3. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations^4-8. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network⁹. For networks with only spatially localized entanglement at each node, the noise performance of the network improves at best with the square root of the number of nodes¹⁰. Here we demonstrate that spatially distributed entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 decibels better precision than one without spatially distributed entanglement, and 11.6 decibels improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs.

Quantum enhanced multiple-phase estimation with multi-mode N00N states

Quantum metrology can achieve enhanced sensitivity for estimating unknown parameters beyond the standard quantum limit. Recently, multiple-phase estimation exploiting quantum resources has attracted intensive interest for its applications in quantum imaging and sensor networks. For multiple-phase estimation, the amount of enhanced sensitivity is dependent on quantum probe states, and multi-mode N00N states are known to be a key resource for this. However, its experimental demonstration has been missing so far since generating such states is highly challenging. Here, we report generation of multi-mode N00N states and experimental demonstration of quantum enhanced multiple-phase estimation using the multi-mode N00N states. In particular, we show that the quantum Cramer-Rao bound can be saturated using our two-photon four-mode N00N state and measurement scheme using a 4 × 4 multi-mode beam splitter. Our multiple-phase estimation strategy provides a faithful platform to investigate multiple parameter estimation scenarios.

Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox

The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.

Quantum Plasmonic Sensors

The extraordinary sensitivity of plasmonic sensors is well-known in the optics and photonics community. These sensors exploit simultaneously the enhancement and the localization of electromagnetic fields close to the interface between a metal and a dielectric. This enables, for example, the design of integrated biochemical sensors at scales far below the diffraction limit. Despite their practical realization and successful commercialization, the sensitivity and associated precision of plasmonic sensors are starting to reach their fundamental classical limit given by quantum fluctuations of light-known as the shot-noise limit. To improve the sensing performance of these sensors beyond the classical limit, quantum resources are increasingly being employed. This area of research has become known as "quantum plasmonic sensing", and it has experienced substantial activity in recent years for applications in chemical and biological sensing. This review aims to cover both plasmonic and quantum techniques for sensing, and it shows how they have been merged to enhance the performance of plasmonic sensors beyond traditional methods. We discuss the general framework developed for quantum plasmonic sensing in recent years, covering the basic theory behind the advancements made, and describe the important works that made these advancements. We also describe several key works in detail, highlighting their motivation, the working principles behind them, and their future impact. The intention of the review is to set a foundation for a burgeoning field of research that is currently being explored out of intellectual curiosity and for a wide range of practical applications in biochemistry, medicine, and pharmaceutical research.

Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields

We explore a class of quantum control operations based on a wide family of harmonic magnetic fields that vary softly in time. Depending on the magnetic field amplitudes taking part, these control operations can produce either squeezing or loop (orbit) effects, and even parametric resonances, on the canonical variables. For these purposes we focus our attention on the evolution of observables whose dynamical picture is ascribed to a quadratic Hamiltonian that depends explicitly on time. In the first part of this work we survey such operations in terms of biharmonic magnetic fields. The dynamical analysis is simplified using a stability diagram in the amplitude space, where the points of each region will characterise a specific control operation. We discuss how the evolution loop effects are formed by fuzzy (non-commutative) trajectories that can be closed or open, in the latter case, even hiding some features that can be used to manipulate the operational time. In the second part, we generalise the case of biharmonic fields and translate the discussion to the case of polyharmonic fields. Using elementary properties of the Toeplitz matrices, we can derive exact solutions of the problem in a symmetric evolution interval, leading to the temporal profile of those magnetic fields suitable to achieve specific control operations. Some of the resulting fuzzy orbits can be destroyed by the influence of external forces, while others simply remain stable.