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Quantum sensing has become a mature and broad field. It is generally related with the idea of using quantum resources to boost the performance of a number of practical tasks, including the radar-like detection of faint objects, the readout of information from optical memories or fragile physical systems, and the optical resolution of extremely close point-like sources. Here we first focus on the basic tools behind quantum sensing, discussing the most recent and general formulations for the problems of quantum parameter estimation and hypothesis testing. With this basic background in our hands, we then review emerging applications of quantum sensing in the photonic regime both from a theoretical and experimental point of view. Besides the state-of-the-art, we also discuss open problems and potential next steps.

Squeezed light generation has come of age. Significant advances on squeezed light generation has been made over the last 30 years -from the initial, conceptual experiment in 1985 till todays toptuned, application-oriented setups. Here we review the main experimental platforms for generating quadrature squeezed light that has been investigated the last 30 years.

Secret communication over public channels is one of the central pillars of a modern information society. Using quantum key distribution this is achieved without relying on the hardness of mathematical problems, which might be compromised by improved algorithms or by future quantum computers. State-of-the-art quantum key distribution requires composable security against coherent attacks for a finite number of distributed quantum states as well as robustness against implementation side channels. Here we present an implementation of continuous-variable quantum key distribution satisfying these requirements. Our implementation is based on the distribution of continuous-variable Einstein–Podolsky–Rosen entangled light. It is one-sided device independent, which means the security of the generated key is independent of any memoryfree attacks on the remote detector. Since continuous-variable encoding is compatible with conventional optical communication technology, our work is a step towards practical implementations of quantum key distribution with state-of-the-art security based solely on telecom components.

Networking plays a ubiquitous role in quantum technology [1, 2]. It is an integral part of quantum communication and has significant potential for upscaling quantum computer technologies that are otherwise not scalable [3]. Recently, it was realized that sensing of multiple spatially distributed parameters may also benefit from an entangled quantum network [4][5][6][7][8][9]. Here we experimentally demonstrate how sensing of an averaged phase shift among four distributed nodes benefits from an entangled quantum network. Using a four-mode entangled continuous variable (CV) state, we demonstrate deterministic quantum phase sensing with a precision beyond what is attainable with separable probes. The techniques behind this result can have direct applications in a number of primitives ranging from biological imaging to quantum networks of atomic clocks.Quantum noise associated with quantum states of light and matter ultimately limits the precision by which measurements can be carried out [10][11][12]. However, by carefully designing the coherence of this quantum noise to exhibit properties such as entanglement and squeezing, it is possible to measure various physical parameters with significantly improved sensitivity compared to classical sensing schemes. Numerous realizations of quantum sensing utilizing non-classical states of light [2,13,15] and matter [16] have been reported, while only a few applications have been explored. Examples are quantum-enhanced gravitational waves interferometry [17], detection of magnetic fields [18][19][20] and sensing of the viscous-elasticity parameter of yeast cells [21]. All these implementations are, however, restricted to the sensing of a single parameter at a single location.Spatially distributed sensing of parameters at multiple locations in a network is relevant for applications from local beam tracking [22] to global scale clock synchronization [4]. The development of quantum networks [1, 2,23,24] enables new strategies for enhanced performance in such scenarios. Theoretical works [5][6][7][8][25][26][27][28] have shown that entanglement can improve sensing capabilities in a network using either twin-photons * or Greenberger-Horne-Zeilinger (GHZ) states combined with photon number resolving detectors [6,7] or using CV entanglement for the detection of distributed phase space displacements [8]. In this Letter, we experimentally demonstrate an entangled CV network for sensing of multiple phase shifts inspired by the theoretical proposal of Ref. [8]. Moreover, for the first time in any system, we demonstrate deterministic distributed sensing in a network of four nodes with a sensitivity beyond that achievable with a separable approach using similar quantum states. BSN … vaccum vaccum S a b c d FIG. 1.Distributed phase sensing scheme. The task is to estimate the average value of M spatially distributed phase shifts φ1, . . . , φM . (a) Without a network, the average phase shift must be estimated by probing each sample individually. This can be done with homodyne detection of the...

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Optical phase estimation is a vital measurement strategy that is used to perform accurate measurements of various physical quantities including length, velocity and displacements 1,2 . The precision of such measurements can be greatly enhanced by the use of entangled or squeezed states of light as demonstrated in a variety of different optical systems [3][4][5][6][7][8] . Most of these accounts, however, deal with the measurement of a very small shift of an already known phase, which is in stark contrast to ab initio phase estimation where the initial phase is unknown [9][10][11][12] . Here, we report on the realization of a quantum-enhanced and fully deterministic ab initio phase estimation protocol based on real-time feedback control. Using robust squeezed states of light combined with a real-time Bayesian adaptive estimation algorithm, we demonstrate deterministic phase estimation with a precision beyond the quantum shot noise limit. The demonstrated protocol opens up new opportunities for quantum microscopy, quantum metrology and quantum information processing.Parameter estimation is an integral part of any physical experiment. In some cases, the parameter under interrogation can be measured sharply and thus the uncertainty associated with the measurement is solely governed by the fluctuations of the parameter itself. In other cases, a sharp, canonical measurement cannot be realized even in principle. The optical phase is an example of such a parameter 13 . Because of the immense importance of performing accurate phase measurements in imaging, metrology and communications applications, numerous theoretical proposals for designing optimized phase measurements have been put forward. The basic aim is to devise a scheme that achieves the sharpest probability distribution for the phase measurement given a fixed amount of resources.Quantum estimation theory provides the ultimate bounds on the variance of such a probability distribution 14,15 in the form of the Cramer-Rao theorem 16,17 : given N probe states, the variance of any unbiased estimatorf is bounded from below by the quantitieswhere F(ϕ) is the Fisher information (FI), which is a measure of the phase information associated with a certain detection strategy, and the quantum Fisher information (QFI) H is the maximized FI over all possible detection strategies. The ultimate lower bound on the variance off , 1/NH, is called the quantum Cramer-Rao (QCR) bound and 1/NF(ϕ) is known as the Cramer-Rao (CR) bound.Using coherent states of light, the QFI is proportional to the mean number of photons, H = 4⟨n⟩, and thus the QCR bound is given by V = 1/4N⟨n⟩, the so-called shot noise limit. This limit is superior to the standard quantum limit (SQL), which is given by V = 1/2N⟨n⟩ and realized with a heterodyne detector 18 . The SQL has been surpassed in previous experiments using adaptive measurements of a coherent state 19,20 .Using non-classical resources, the estimation sensitivity can be greatly enhanced beyond the shot noise limit and eventually reach the optimal H...