The light produced by parametric down-conversion shows strong spatial entanglement that leads to violations of EPR criteria for separability. Historically, such studies have been performed by scanning a single-element, single-photon detector across a detection plane. Here we show that modern electron-multiplying charge-coupled device cameras can measure correlations in both position and momentum across a multi-pixel field of view. This capability allows us to observe entanglement of around 2,500 spatial states and demonstrate Einstein–Podolsky–Rosen type correlations by more than two orders of magnitude. More generally, our work shows that cameras can lead to important new capabilities in quantum optics and quantum information science.

Correlated photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments, two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated photon ghost imaging experiments have scanned a single-pixel detector through the field of view to obtain spatial information. However, scanning leads to poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work, we overcome this limitation by using a time-gated camera to record the singlephoton events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far field of the photon pair source, taking advantage of the Einstein-Podolsky-Rosen-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing.

Conventional imaging systems rely upon illumination light that is scattered or transmitted by the object and subsequently imaged. Ghost-imaging systems based on parametric downconversion use twin beams of position-correlated signal and idler photons. One beam illuminates an object while the image information is recovered from a second beam that has never interacted with the object. In this Letter, we report on a camera-based ghost imaging system where the correlated photons have significantly different wavelengths. Infrared photons at 1550 nm wavelength illuminate the object and are detected by an InGaAs/InP single-photon avalanche diode. The image data are recorded from the coincidently detected, position-correlated, visible photons at a wavelength of 460 nm using a highly efficient, low-noise, photon-counting camera. The efficient transfer of the image information from infrared illumination to visible detection wavelengths and the ability to count single photons allows the acquisition of an image while illuminating the object with an optical power density of only 100 pJ cm −2 s −1 . This wavelengthtransforming ghost-imaging technique has potential for the imaging of light-sensitive specimens or where covert operation is desired. Low-light-level imaging at infrared wavelengths has many applications within both the technological and biological sectors. These applications span covert security systems, the imaging of light-sensitive biological samples, and imaging within semiconductor devices. However, given that the majority of single-photon-sensitive, large-format detector arrays are siliconbased and therefore ineffective at wavelengths greater than 1 μm, the technological difficulties with such applications are readily apparent: crafting a camera with high quantum efficiency and low noise at infrared wavelengths is difficult and expensive.In this Letter, we circumvent the lack of infrared cameras that combine low-noise with single-photon sensitivity by performing the imaging using the so-called "ghost imaging" method. This method utilizes the spatial correlations between photons in the two output beams, signal and idler, generated through the spontaneous parametric down-conversion (SPDC) process [1].In the 1990s, it was shown how the correlations between photons generated through SPDC could be utilized to create imaging systems [2,3]. These ghost-imaging systems rely on the strong position correlations between the beams of signal and idler photons that are produced by the SPDC process [4]. In a ghost-imaging system a transmissive object is placed in the idler beam and the transmitted photons are measured using a single-element, heralding detector. The use of a single-element detector means that measurements of photons that probe the object reveal no spatial information. In parallel to these measurements of the idler photons, a scanning single-element detector measures the corresponding signal photons-but since these signal photons do not interact with the object, again no image is formed. However, although the ...

The propagation of transverse spatial correlations of photon pairs through arbitrary first-order linear optical systems is studied experimentally and theoretically using the fractional Fourier transform. Highly-correlated photon pairs in an EPR-like state are produced by spontaneous parametric down-conversion and subject to optical fractional Fourier transform systems. It is shown that the joint detection probability can display either correlation, anti-correlation, or no correlation, depending on the sum of the orders $\alpha$ and $\beta$ of the transforms of the down-converted photons. We present analytical results for the propagation of the perfectly correlated EPR state, and numerical results for the propagation of the two-photon state produced from parametric down-conversion. We find good agreement between theory and experiment.Comment: 9 pages, 7 figures, to appear PR

We discuss the use of the transverse spatial degrees of freedom of photons propagating in the paraxial approximation for continuous-variable information processing. Given the wide variety of linear optical devices available, a diverse range of operations can be performed on the spatial degrees of freedom of single photons. Here we show how to implement a set of continuous quantum logic gates which allow for universal quantum computation. In contrast with the usual quadratures of the electromagnetic field, the entire set of single-photon gates for spatial degrees of freedom does not require optical nonlinearity and, in principle, can be performed with a single device: the spatial light modulator. Nevertheless, nonlinear optical processes, such as four-wave mixing, are needed in the implementation of two-photon gates. The efficiency of these gates is at present very low; however, small-scale investigations of continuous-variable quantum computation are within the reach of current technology. In this regard, we show how novel cluster states for one-way quantum computing can be produced using spontaneous parametric down-conversion.

Transverse entanglement between pairs of photons can be detected through intensity correlation measurements in the near and far fields. We show theoretically and experimentally that at intermediate zones, it is also possible to detect transverse entanglement performing only intensity correlation measurements. Our results are applicable to a number of physical systems.Comment: 4 pages, 3 figures. accepted for publication in Phys. Rev. A Rapid Com

The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.Introduction. The ability to measure a system in an infinite number of non-commuting bases distinguishes the quantum world from classical physics. Wave-particle duality and more generally the complementarity principle are directly rooted in this feature of quantum mechanics. Though one can measure a quantum system in several distinct bases, uncertainty relations limit the amount of information that can be obtained. It is well known that projection onto an eigenstate of one basis reduces the information that can be obtained through or inferred about subsequent measurement in a different basis. The information is minimum for mutually unbiased bases (MUBs), for which all outcomes of the second measurement are equally likely, so that total uncertainty is always substantial (the sharpest uncertainty relations [1]) and most insensitive to input states [2]. MUBs play an important role in complementarity [3], quantum cryptography [4] and quantum tomography [5,6], are useful for certifying quantum randomness [7], and for detecting quantum correlations such as entanglement [8][9][10] and steering [11][12][13][14][15][16][17][18].

We derive reliable entanglement witnesses for coarse-grained measurements on continuous variable systems. These witnesses never return a "false positive" for identification of entanglement, under any degree of coarse graining. We show that even in the case of Gaussian states, entanglement witnesses based on the Shannon entropy can outperform those based on variances. We apply our results to experimental identification of spatial entanglement of photon pairs.