The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root of the number of repetitions. Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches. In this Review, we analyse some of the most promising recent developments of this research field and point out some of the new experiments. We then look at one of the major new trends of the field: analyses of the effects of noise and experimental imperfections.

Advances in quantum metrology

Entangled quantum states are not separable, regardless of the spatial separation of their components This is a manifestation of an aspect of quantum mechanics known as quantum non-locality An important consequence of this is that the measurement of the state of one particle in a two-particle entangled state defines the state of the second particle instantaneously, whereas neither particle possesses its own well-defined state before the measurement Experimental realizations of entanglement have hitherto been restricted to two-state quantum systems, involving, for example, the two orthogonal polarization states of photons Here we demonstrate entanglement involving the spatial modes of the electromagnetic field carrying orbital angular momentum As these modes can be used to define an infinitely dimensional discrete Hilbert space, this approach provides a practical route to entanglement that involves many orthogonal quantum states, rather than just two Multi-dimensional entangled states could be of considerable importance in the field of quantum information, enabling, for example, more efficient use of communication channels in quantum cryptography

Entanglement of the orbital angular momentum states of photons

Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. The original theory and its improvements are reviewed, and a few examples of experimental two-qubit gates are given. The use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.

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Linear optical quantum computing with photonic qubits

The first quantum technology that harnesses quantum mechanical effects for its core operation has arrived in the form of commercially available quantum key distribution systems. This technology achieves enhanced security by encoding information in photons such that an eavesdropper in the system can be detected. Anticipated future quantum technologies include large-scale secure networks, enhanced measurement and lithography, and quantum information processors, which promise exponentially greater computational power for particular tasks. Photonics is destined to have a central role in such technologies owing to the high-speed transmission and outstanding low-noise properties of photons. These technologies may use single photons, quantum states of bright laser beams or both, and will undoubtedly apply and drive state-of-the-art developments in photonics.

Photonic quantum technologies

"Quantum sensing" describes the use of a quantum system, quantum properties or quantum phenomena to perform a measurement of a physical quantity Historical examples of quantum sensors include magnetometers based on superconducting quantum interference devices and atomic vapors, or atomic clocks More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology, with the most common platforms being spin qubits, trapped ions and flux qubits The field is expected to provide new opportunities - especially with regard to high sensitivity and precision - in applied physics and other areas of science In this review, we provide an introduction to the basic principles, methods and concepts of quantum sensing from the viewpoint of the interested experimentalist

Quantum sensing

Superposition is one of the most distinctive features of quantum theory and has been demonstrated in numerous single-particle interference experiments. Quantum entanglement, the coherent superposition of states in multi-particle systems, yields more complex phenomena. One important type of multi-particle experiment uses path-entangled number states, which exhibit pure higher-order interference and the potential for applications in metrology and imaging; these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit, or quantum lithography beyond the classical diffraction limit. It has been generally understood that in optical implementations of such schemes, lower-order interference effects always decrease the overall performance at higher particle numbers. Such experiments have therefore been limited to two photons. Here we overcome this limitation, demonstrating a four-photon interferometer based on linear optics. We observe interference fringes with a periodicity of one-quarter of the single-photon wavelength, confirming the presence of a four-particle mode-entangled state. We anticipate that this scheme should be extendable to arbitrary photon numbers, holding promise for realizable applications with entanglement-enhanced performance.

De Broglie wavelength of a non-local four-photon state

We experimentally demonstrate observation of highly pure four-photon GHZ entanglement produced by parametric down-conversion and a projective measurement. At the same time this also demonstrates teleportation of entanglement with very high purity. Not only does the achieved high visibility enable various novel tests of quantum nonlocality, it also opens the possibility to experimentally investigate various quantum computation and communication schemes with linear optics. Our technique can, in principle, be used to produce entanglement of arbitrarily high order or, equivalently, teleportation and entanglement swapping over multiple stages.

https://arxiv.org/pdf/quant-ph/0104047.pdf

Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation

Distribution of entangled states between distant locations is essential for quantum communication1,2,3 over large distances. But owing to unavoidable decoherence in the quantum communication channel, the quality of entangled states generally decreases exponentially with the channel length. Entanglement purification4,5—a way to extract a subset of states of high entanglement and high purity from a large set of less entangled states—is thus needed to overcome decoherence. Besides its important application in quantum communication, entanglement purification also plays a crucial role in error correction for quantum computation, because it can significantly increase the quality of logic operations between different qubits6. Here we demonstrate entanglement purification for general mixed states of polarization-entangled photons using only linear optics7. Typically, one photon pair of fidelity 92% could be obtained from two pairs, each of fidelity 75%. In our experiments, decoherence is overcome to the extent that the technique would achieve tolerable error rates for quantum repeaters in long-distance quantum communication8. Our results also imply that the requirement of high-accuracy logic operations in fault-tolerant quantum computation can be considerably relaxed6.

Experimental entanglement purification of arbitrary unknown states

We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed forwardable. In the experiment, we achieved this goal with only the use of linear optics, an entangled ancillary pair of photons, and postselection. The techniques developed in our experiment are of significant importance for quantum information processing with linear optics.

https://www.univie.ac.at/qfp/publications3/pdffiles/2004-07.pdf

Realization of a photonic controlled-NOT gate sufficient for quantum computation.

Quantum teleportation1 is central to quantum communication, and plays an important role in a number of quantum computation protocols2,3. Most information-processing applications of quantum teleportation include the subsequent manipulation of the qubit (the teleported photon), so it is highly desirable to have a teleportation procedure resulting in high-quality, freely flying qubits. In our previous teleportation experiment4, the teleported qubit had to be detected (and thus destroyed) to verify the success of the procedure. Here we report a teleportation experiment that results in freely propagating individual qubits. The basic idea is to suppress unwanted coincidence detection events by providing the photon to be teleported much less frequently than the auxiliary entangled pair. Therefore, a case of successful teleportation can be identified with high probability without the need actually to detect the teleported photon. The experimental fidelity of our procedure surpasses the theoretical limit required for the implementation of quantum repeaters5,6.

Sara Gasparoni

Papers

De Broglie wavelength of a non-local four-photon state

Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation

Experimental entanglement purification of arbitrary unknown states

Realization of a photonic controlled-NOT gate sufficient for quantum computation.

Experimental realization of freely propagating teleported qubits.