Multiphoton interference reveals strictly nonclassical phenomena. Its applications range from fundamental tests of quantum mechanics to photonic quantum information processing, where a significant fraction of key experiments achieved so far comes from multiphoton state manipulation. The progress, both theoretical and experimental, of this rapidly advancing research is reviewed. The emphasis is given to the creation of photonic entanglement of various forms, tests of the completeness of quantum mechanics (in particular, violations of local realism), quantum information protocols for quantum communication (e.g., quantum teleportation, entanglement purification, and quantum repeater), and quantum computation with linear optics. The scope of the review is limited to ``few-photon'' phenomena involving measurements of discrete observables.

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Multiphoton entanglement and interferometry

Quantum states of light, such as squeezed states or entangled states, can be used to make measurements (metrology), produce images, and sense objects with a precision that far exceeds what is possible classically, and also exceeds what was once thought to be possible quantum mechanically. The primary idea is to exploit quantum effects to beat the shot-noise limit in metrology and the Rayleigh diffraction limit in imaging and sensing. Quantum optical metrology has received a boost in recent years with an influx of ideas from the rapidly evolving field of optical quantum information processing. Both areas of research exploit the creation and manipulation of quantum-entangled states of light. We will review some of the recent theoretical and experimental advances in this exciting new field of quantum optical metrology, focusing on examples that exploit a particular two-mode entangled photon state – the High-N00N state.

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Quantum optical metrology – the lowdown on high-N00N states

Quantum states of light, such as squeezed states or entangled states, can be used to make measurements (metrology), produce images, and sense objects with a precision that far exceeds what is possible classically, and also exceeds what was once thought to be possible quantum mechanically. The primary idea is to exploit quantum effects to beat the shot-noise limit in metrology and the Rayleigh diffraction limit in imaging and sensing. Quantum optical metrology has received a boost in recent years with an influx of ideas from the rapidly evolving field of optical quantum information processing. Both areas of research exploit the creation and manipulation of quantum-entangled states of light. We will review some of the recent theoretical and experimental advances in this exciting new field of quantum optical metrology, focusing on examples that exploit a particular two-mode entangled photon state -- the High-N00N state.

Quantum Optical Metrology -- The Lowdown on High-N00N States

Spatial correlations in parametric down-conversion

Entanglement is an important resource for quantum technologies. There are many ways quantum systems can be entangled, ranging from the two-qubit case to entanglement in high dimensions or between many parties. Consequently, many entanglement quantifiers and classifiers exist, corresponding to different operational paradigms and mathematical techniques. However, for most quantum systems, exactly quantifying the amount of entanglement is extremely demanding, if at all possible. Furthermore, it is difficult to experimentally control and measure complex quantum states. Therefore, there are various approaches to experimentally detect and certify entanglement when exact quantification is not an option. The applicability and performance of these methods strongly depend on the assumptions regarding the involved quantum states and measurements, in short, on the available prior information about the quantum system. In this Review, we discuss the most commonly used quantifiers of entanglement and survey the state-of-the-art detection and certification methods, including their respective underlying assumptions, from both a theoretical and an experimental point of view. Entanglement is often considered the defining feature separating classical physics from quantum physics and provides the basis for many quantum technologies. This Review discusses recent progress in the challenging task of conclusively proving that a physical system features entanglement, surveying detection and certification methods.

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Entanglement certification from theory to experiment

We demonstrate a simple experimental method for creating entangled qudits. Using transverse-momentum and position entanglement of photons emitted in spontaneous parametric down-conversion, we show entanglement between discrete regions of space, i.e., pixels. We map each photon onto as many as six pixels, where each pixel represents one level of our qudit state. The method is easily generalizable to create even higher dimensional, entangled states. Thus, the realization of quantum information processing in arbitrarily high dimensions is possible, allowing for greatly increased information capacity.

Pixel entanglement: experimental realization of optically entangled d=3 and d=6 qudits.

A nonlinear optical, phase-shifted-grating method for improving the resolution of feature sizes is implemented experimentally using an N-photon lithographic material. For the recording medium, we used poly(methyl-methacrylate) (PMMA), which is a UV lithographic material that can be excited by multi-photon absorption in the visible region. We achieved a two-fold enhancement of the resolution over the standard Rayleigh limit of half of the wavelength.

Implementation of sub-Rayleigh-resolution lithography using an N-photon absorber

We demonstrate a method for creating entangled qudits using momentum and position entanglement in spontaneous parametric down-conversion. We image each photon onto an array of pixels, each representing one level of the qudit state.

Pixel entanglement: experimental realization of optically entangled d=3 and d=6 qudits

We demonstrate a direct measurement of thickness gradients in vertical soap films with a resonant differential interferometer, i.e., the Jamin-Fabry-Perot interferometer. Two regimes are investigated: thick colored films with gravity- and capillarity-induced gradients, and silvery-gray to common black films which are quasi-independent of gravity. In the colored zone, our differential method is an ideal tool with which to isolate the large thickness instabilities of the film reaching 17nm∕mm that characterize the end of its drainage. Using the so-called F2 law of such an interferometer, thermal-induced thickness variations as small as 1nm are isolated in the gradient-free common black film.

Dynamics of gravity-induced gradients in soap film thicknesses

We study the entanglement of transverse spatial coordinates of biphotons propagating through a turbulent medium. The degree of entanglement is quantified by calculating the second moments of the spatial coordinates.

Malcolm N. O'Sullivan-Hale

Papers

Pixel entanglement: experimental realization of optically entangled d=3 and d=6 qudits.

Implementation of sub-Rayleigh-resolution lithography using an N-photon absorber

Pixel entanglement: experimental realization of optically entangled d=3 and d=6 qudits

Dynamics of gravity-induced gradients in soap film thicknesses

Entanglement Degradation of Biphotons Propagating in Turbulent Medium