Quantum walks of correlated particles offer the possibility to study large-scale quantum interference, simulate biological, chemical and physical systems, and a route to universal quantum computation. Here we demonstrate quantum walks of two identical photons in an array of 21 continuously evanescently-coupled waveguides in a SiOxNy chip. We observe quantum correlations, violating a classical limit by 76 standard deviations, and find that they depend critically on the input state of the quantum walk. These results open the way to a powerful approach to quantum walks using correlated particles to encode information in an exponentially larger state space.With origins dating back to observations by Lucretius in 60BC and Brown in the 1800's, random walks are a powerful tool used in a broad range of fields from genetics to economics [1]. The quantum mechanical analoguequantum walks [2, 3]-corresponds to the tunnelling of quantum particles into several possible sites, generating large coherent superposition states and allowing massive parallelism in exploring multiple trajectories through a given connected graph (eg. Fig. 1). This quantum state evolution is a reversible (unitary) process and so requires low noise (decoherence) systems for observation. In contrast to the diffusive behaviour of (classical) random walks, which tend towards a steady state, the wave function in a quantum walk propagates ballistically (Fig. 2(c)). These features are at the heart of new algorithms for database-search [4], random graph navigation, models for quantum communication using spin chains [5], universal quantum computation [6] and quantum simulation [7].Quantum walks have been demonstrated using nuclear magnetic resonance [8,9], phase [10,11] and position [12] space of trapped ions, the frequency space of an optical resonator [13], single photons in bulk [14] and fibre [15] optics and the scattering of light in coupled waveguide arrays [16]. However, to date, all realisations have been limited to single particle quantum walks, which have an exact mapping to classical wave phenomena [17], and therefore cannot provide any advantage from quantum effects (note that the quantum walk with two trapped ions [11] encodes in the centre of mass mode and is therefore effectively a single particle quantum walk on a line). Indeed single particle quantum walks have been observed using classical light [16,18]. In contrast, for quantum walks of more than one indistinguishable particle, classical theory no longer provides a sufficient description-quantum theory predicts that probability amplitudes interfere leading to distinctly non-classical correlations [19,20]. This quantum behaviour gives rise to a computational advantage in quantum walks of two identical particles, which can be used to solve the graph isomorphism problem for example [21]. The major challenge associated with realising quantum walks of correlated particles is the need for a low decoherence system that preserves their non-classical features.The intrinsically low decoherence properti...
We describe an advanced image reconstruction algorithm for pseudothermal ghost imaging, reducing the number of measurements required for image recovery by an order of magnitude. The algorithm is based on compressed sensing, a technique that enables the reconstruction of an N -pixel image from much less than N measurements. We demonstrate the algorithm using experimental data from a pseudothermal ghost-imaging setup. The algorithm can be applied to data taken from past pseudothermal ghost-imaging experiments, improving the reconstruction's quality.Ghost imaging (GI) has emerged a decade ago as an imaging technique which exploits the quantum nature of light, and has been in the focus of many studies since [1, and references therin]. In GI an object is imaged even though the light which illuminates it is collected by a single-pixel detector which has no spatial resolution (a bucket detector). This is done by correlating the intensities measured by the bucket detector with an image of the eld which impinges upon the object. GI was originally performed using entangled photon pairs [2], and later on was realized with classical light sources [3,4,5,6]. The demonstrations of GI with classical light sources, and especially pseudothermal sources, triggered an ongoing e ort to implement GI for various sensing applications [4,7]. However, one of the main drawbacks of pseudothermal GI is the long acquisition times required for reconstructing images with a good signal-to-noise ratio (SNR) [1,8].In this work we propose an advanced reconstruction algorithm for pseudothermal GI, which reduces signicantly the required acquisition times. The algorithm is based on compressed sensing (or compressive sampling, CS) [9,10], an advanced sampling and reconstruction technique which has been recently implemented in several elds of imaging. Examples for such are magnetic resonance imaging [11], astronomy [12], THz imaging [13], and single-pixel cameras [14]. The main idea behind CS is to exploit the redundancy in the structure of most natural signals/objects to reduce the number of measurements required for faithful reconstruction. Here we show that applying a CS-based reconstruction algorithm to data taken from conventional pseudothermal GI measurements dramatically improves the SNR of the reconstructed images and thus allows for shorter acquisition times.In conventional pseudothermal GI, an object is illuminated by a speckle eld generated by passing a laser beam through a rotating di user [ Fig. 1(a)]. For each phase realization r of the di user, the speckle eld I r (x, y) which impinges on the object is imaged. This is done by splitting the beam before the object to an 'object arm' and a 'reference arm', and placing a CCD camera at the refer- * Electronic address: ori.katz@weizmann.ac.il Figure 1: (Color online) (a) Standard pseudothermal GI twodetectors setup. A copy of the speckle eld which impinges on the object is imaged with a CCD camera, and correlated with the intensity measured by a bucket detector. (b) The computational GI singl...
Complex optical photon states with entanglement shared among several modes are critical to improving our fundamental understanding of quantum mechanics and have applications for quantum information processing, imaging, and microscopy. We demonstrate that optical integrated Kerr frequency combs can be used to generate several bi- and multiphoton entangled qubits, with direct applications for quantum communication and computation. Our method is compatible with contemporary fiber and quantum memory infrastructures and with chip-scale semiconductor technology, enabling compact, low-cost, and scalable implementations. The exploitation of integrated Kerr frequency combs, with their ability to generate multiple, customizable, and complex quantum states, can provide a scalable, practical, and compact platform for quantum technologies.
We experimentally demonstrate pseudothermal ghost imaging and ghost diffraction using only a single single-pixel detector. We achieve this by replacing the high resolution detector of the reference beam with a computation of the propagating field, following a recent proposal by Shapiro [J. H. Shapiro, arXiv:0807.2614 (2008)]. Since only a single detector is used, this provides an experimental evidence that pseudothermal ghost imaging does not rely on non-local quantum correlations. In addition, we show the depth-resolving capability of this ghost imaging technique.Comment: See video at http://www.weizmann.ac.il/home/feori/Misc.html Comments are welcom
We study quantum and classical Hanbury Brown-Twiss correlations in waveguide lattices. We develop a theory for the propagation of photon pairs in the lattice, predicting the emergence of nontrivial quantum interferences unique to lattice systems. Experimentally, we observe the classical counterpart of these interferences using intensity-correlation measurements. We discuss the correspondence between the classical and quantum correlations, and consider path-entangled input states which do not have a classical analogue. Our results demonstrate that waveguide lattices can be used as a robust and highly controllable tool for manipulating quantum states, and offer new ways of studying the quantum properties of light.
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