Multipath Entanglement of Two Photons

Abstract

We present a novel optical device based on an integrated system of micro-lenses and single mode optical fibers. It allows to collect and direct into many modes two photons generated by spontaneous parametric down conversion. By this device multiqubit entangled states and/or multilevel qu-dit states of two photons, encoded in the longitudinal momentum degree of freedom, are created. The multi-path photon entanglement realized by this device is expected to find important applications in modern quantum information technology. Entangling two photons in a high-dimension Hilbert space allows the realization of important quantum information tasks. These deal with a complete analysis of Bell states [1,2,3] and novel protocols of superdense coding [4], the possibility to perform secure quantum cryptography [5,6] and a fast, high-fidelity one-way quantum computation [7], [8,9,10,11], besides the realization of novel quantum nonlocality tests [12,13,14,15].Multidimensional entangled states of two photons have been realized by engineering both qu-dit states and hyperentangled (HE) states. In the former each particle belongs to a d-level quantum system, in the latter the particles are entangled in more than one degree of freedom (DOF). Since a qu-dit, with d = 2 N , is equivalent to N qubits, two-entangled qu-dits are equivalent to the HE state of two particles entangled in N DOFs. Polarization, time bin and spatial entanglement have been adopted to create qu-dits with d = 3 [6,16], d = 4 [17] and d = 8 [18]. At the same time, HE states have been realized by using in different ways polarization, longitudinal momentum and orbital angular momentum, besides time-bin entanglement [1,19,20,21,22].In this paper we present the first experimental realization of a quantum state of two photons entangled in many optical paths. It is based on the spontaneous parametric down conversion (SPDC) emission of a Type I phase-matched nonlinear (NL) crystal operating under the excitation of a continuous wave (cw) laser at wavelength (wl) λ p . In these conditions, the degenerate signal (s) and idler (i) photons, are generated with uniform probability distribution, at wl λ s = λ i = 2λ p , over a continuum of correlated k-modes belonging to the lateral surface of a cone. Usually, no more than two correlated spatial modes are used in experiments based on Type I crystals, hence the main part of SPDC radiation is lost. By exploiting the continuum of k-mode emission of Type * URL: http://quantumoptics.phys.uniroma1.it/ I crystals, high-dimension entangled states can be created [23]. Indeed, a very large number of qubits are in principle available by this geometry. However, a successfull realization of this idea strongly depends on the possibility to overcome the practical difficulties represented by independently collecting and manipulating the SPDC radiation belonging to a large number of k-modes.By the device realized in this experiment, photon pairs travelling along a large number of k-modes are efficiently coupled into a bundle of single mode opt...

Quantum computation mediated by ancillary qudits and spin coherent states

“…Physical systems that are used as qubits are often restrictions of higher dimensional systems to a two-dimensional subspace and hence many of these systems are naturally suited to a d-level qudit structure [45]. Qudits have been demonstrated in various physical systems, including superconducting [46], atomic [47], and photonic systems, where in the latter the qudit is encoded in the linear [48,49] or orbital angular momentum [50] of a single photon. A further possible realization of a qudit is in the Fock states of a field mode which can be coupled to individual qubits via the Jaynes-Cummings model [51].…”

Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information

“…After characterization of the reversed MS as an interface between the lateral position and OAM, we demonstrate its use in quantum optical experiments and transform a bipartite path-entangled state to an OAM-entangled state, even for higher-dimensional states. We create pairs of orthogonally polarized, path-entangled photons from position correlation in a spontaneous parametric down-conversion process 2,28,29 (Fig. 4a and Methods).…”

“…A popular approach to increase the complexity of the set-up and the dimensionality of the observed system uses integration of optical elements on photonic chips. On these chips the most convenient way of encoding information is the path of the photons, which is inherently extendable to higher-dimensional systems 2,3 . Another possibility of encoding high-dimensional quantum information is the transverse spatial mode of light 4 .…”

Generation and confirmation of a (100 × 100)-dimensional entangled quantum system

“…There, different multilevel degrees of freedom, such as spatial modes (13), time-energy (14), path (15,16), as well as continuous variables (17,18), have been used. Entanglement of spatial modes of photons has especially attracted much attention in recent years (19)(20)(21)(22)(23)(24)(25)(26)(27)(28), because it is readily available from optical nonlinear crystals and the number of involved modes of the entanglement can be very high (29).…”