We report an experiment to generate entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D slits in the arms of the twin photons define the qudit space. By manipulating the pump beam correctly, the twin photons will pass only by symmetrically opposite slits, generating entangled states between these different paths. Experimental results for qudits with D = 4 and 8 are shown. We demonstrate that the generated states are entangled states.

We present the experimental quantum tomography of 7- and 8-dimensional quantum systems based on projective measurements in the mutually unbiased basis (MUB-QT). One of the advantages of MUB-QT is that it requires projections from a minimal number of bases to be performed. In our scheme, the higher dimensional quantum systems are encoded using the propagation modes of single photons, and we take advantage of the capabilities of amplitude- and phase-modulation of programmable spatial light modulators to implement the MUB-QT.

We characterize entanglement in two-qubit pure states encoded in transverse momenta of twin photons obtained from spontaneous parametric down-conversion. Two alternate methods are employed: ͑i͒ measurement of conditional interference patterns and ͑ii͒ measurement of the marginal probability that yields the single-photon interference pattern. Both methods are local with classical communication and rely on Schmidt decomposition of the quantum state, which is generated by letting the photons propagate through an appropriate lens system. In both cases we can obtain the concurrence either through the Schmidt coefficients in the first method or directly relating the concurrence to the visibility of the interference pattern in the second one.

We report an experiment to generate maximally entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D-slits in the arms of the twin photons define the qudit space. By manipulating the pump beam correctly the twin photons will pass only by symmetrically opposite slits, generating entangled states between these different paths. Experimental results for qudits with D = 4 and 8 are shown. We demonstrate that the generated states are entangled states.The interest in studying higher dimensional entangled states comes both from the foundations of quantum mechanics and from the development of new protocols in quantum communication. For instance, it was demonstrated that maximally entangled states of two quantum systems in a D-dimensional Hilbert space, qudits, violate local realism stronger than qubits [1]. Entangled qudits are more resistant to noise than qubits, as was shown in [1,2]. In quantum cryptography [3], the use of entangled qutrits (D = 3) [4,5] or qudits [6,7] instead of qubits is more secure against eavesdropping attacks. Moreover, one knows that the protocols like quantum teleportation [8] or quantum cryptography [3], work best for maximally entangled states. All these facts motivate the development of techniques to generate entangled states among quantum systems in higher dimensional Hilbert space with a good quality of entanglement.Recently, spontaneous parametric down-conversion (SPDC) has been used for realizing entangled qudits. In Ref.[9] four polarization entangled photons are used to obtain two entangled qutrits. The use of two photons in higher dimensional space is another possibility. Entangled qutrits with two photons using an unbalanced 3-arm fiber optic interferometer [10] or photonic orbital angular momentum [11] has been demonstrated. Time-bin entangled qudits up to D = 11 from pump pulses generated by a mode-locked laser has also been reported [12].In this letter, we demonstrate the experimental generation of maximally entangled states of qudits by using the transverse spatial correlations of the photon pairs (biphotons) produced by SPDC. Biphotons are sent through apertures with D-slits. The D possible paths (slits) followed by each photon of the pair are defined as our qudit space. Due to a transference of information from the pump laser beam to the two-photon state [13], we can control the transverse correlations of the photon pairs passing by the slits, by manipulating the pump beam. A proper manipulation of this one allow us to make the biphotons pass only by symmetrically opposite slits, generating entangled states between these different trans-verse spatial modes. Results for qudits with D = 4 and 8 are shown and the scheme described here can be extended to higher dimensions. We give a brief theoretical description of this process and present the experimental results and discussion.Here, it is sufficient to write the equations in one dimension. Considering the degenerate case and us...

Abstract:The study of how to generate high-dimensional quantum states (qudits) is justified by the advantages that they can bring for the field of quantum information. However, to have some real practical potential for quantum communication, these states must be also of simple manipulation. Spatial qudits states, which are generated by engineering the transverse momentum of the parametric down-converted photons, have been until now considered of hard manipulation. Nevertheless, we show in this work a simple technique for modifying these states. This technique is based on the use of programmable diffractive optical devices, that can act as spatial light modulators, to define the Hilbert space of these photons instead of pre-fabricated multi-slits. by Two Entangled N-Dimensional Systems Are Stronger than for Two Qubit," Phys. Rev. Lett. 85, 4418-4421 (2000). 12. J. S. Bell, "On the problem of hidden variables in quantum mechanics," Rev. Mod. Phys. 38, 447-452 (1966). 13. A. Aspect, "Bells inequality test: more ideal than ever," Nature 398, 189-190 (1999

We show that the quantum disentanglement eraser implemented on a two-photon system from parametric down-conversion is a general method to create hybrid photonic entanglement, namely the entanglement between different degrees of freedom of the photon pair. To demonstrate this, we generate and characterize a source with tunable degree of hybrid entanglement between two qubits, one encoded in the transverse momentum and position of a photon, and the other in the polarization of its partner. In addition, we show that a simple extension of our setup enables the generation of two-photon qubit-qudit hybrid entangled states. Finally, we discuss the advantages that this type of entanglement can bring for an optical quantum network.

We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure (POVM) that maximizes our confidence in identifying each state in the set and minimizes the probability of obtaining inconclusive results. The physical realization of this POVM is completely determined and it is shown that after an inconclusive outcome, the input states may be mapped into a new set of equiprobable symmetric states, restricted, however, to a subspace of the original qudit Hilbert space. By applying the MC measurement again onto this new set, we can still gain some information about the input states, although with less confidence than before. This leads us to introduce the concept of "sequential maximum-confidence" (SMC) measurements, where the optimized MC strategy is iterated in as many stages as allowed by the input set, until no further information can be extracted from an inconclusive result. Within each stage of this measurement our confidence in identifying the input states is the highest possible, although it decreases from one stage to the next. In addition, the more stages we accomplish within the maximum allowed, the higher will be the probability of correct identification. We will discuss an explicit example of the optimal SMC measurement applied in the discrimination among four symmetric qutrit states and propose an optical network to implement it.Comment: 14 pages, 4 figures. Published versio

Spatial qudits are D-dimensional (D ≥ 2) quantum systems carrying information encoded in the discretized transverse momentum and position of single photons. We present a proof-of-principle demonstration of a method for preparing arbitrary pure states of such systems by using a single phase-only spatial light modulator (SLM). The method relies on the encoding of the complex transmission function corresponding to a given spatial qudit state onto a preset diffraction order of a phase-only grating function addressed at the SLM. Fidelities of preparation above 94% were obtained with this method, which is simpler, less costly, and more efficient than those that require two SLMs for the same purpose.