Quantum Walks of Correlated Photons

Abstract

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...

Quantum-secure authentication of a physical unclonable key

“…Our light source is an attenuated laser beam chopped into 500 ns light pulses each containing n 230 40 photons. Quantum readout of optical keys can be achieved with single or bi-photon states [13], squeezed states [14], or other fragile quantum states [15]. We use coherent states of light with low mean photon number [16], because in QSA they provide security similar to other quantum states and are easier to implement in real-life applications.…”

The random mass Dirac model and long-range correlations on an integrated optical platform

“…Such photonic lattices have demonstrated their potential as a platform for the implementation of quantum random walks 33,34 , as well as for the quantum simulation of indistinguishable, non-relativistic particles and their exchange statistics 35,36 . By arranging the waveguides in a binary superlattice of alternating high and low refractive index, it is even possible to study the dynamics of relativistic fermions with classical light, such that the light evolution in space is governed by a 1D Dirac equation 37 .…”

“…This further suggests the occurence of long-range correlations in an integrated optical device, even though the interaction between the individual waveguides is only short-ranged. Note that for quantum walks in regular 33,34 or disordered waveguide lattices 44 , jumps between adjacent channels are predominant. Therefore, their correlation functions are always short-ranged, that is, they exhibit exponential slopes.…”

Unidirectional quantum walk of two correlated particles: Manipulating bound-pair and unbound wave-packet components

“…In periodic systems, for example, the quantum particle propagates much faster (ballistic propagation) than its classical counterpart (diffusive propagation) [1]. Quantum walkers have been widely studied in a variety of different settings such as in the development of quantum algorithms [2][3][4], efficient energy transfer in proteins complex [5], classical optics [6,7], waveguide lattices [8,9], nuclear magnetic resonance [10], quantum dots [11], trapped atoms in optical lattices [12,13], disorder [14,15], interacting particles [16,17] and bacteria behavior in biological systems [18].…”