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 study the physical implementation of a qutrit quantum computer in the context of trapped ions. Qutrits are defined in terms of electronic levels of trapped ions. We concentrate our attention on a universal two-qutrit gate, which corresponds to a controlled-NOT gate between qutrits. Using this gate and a general gate of an individual qutrit, any gate can be decomposed into a sequence of these gates. In particular, we show how this works for performing the quantum Fourier transform for n qutrits.

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.

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.

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 propose a cavity-QED scheme for the controlled generation of sequences of entangled singlephoton wavepackets. A photon is created inside a cavity via an active medium, such as an atom, and decays into the continuum of radiation modes outside the cavity. Subsequent wavepackets generated in this way behave as independent logical qubits. This and the possibility of producing maximally entangled multi-qubit states suggest many applications in quantum communication.Pacs number(s): 03.67.Hk, 03.67.-a Sources offering a great variety of entangled states are required for the implementation of many quantum communication and computation protocols [1,2]. With quantum communication [3] in mind the choice of photons as qubits is especially appropriate, since they can be easily transfered over long distances. The standard source presently used in the lab is parametric downconversion in a crystal [4,5]. It is a reliable source of entangled twin-photons but the process is random and largely untailorable. Moreover, in practice its capability of generating entanglement is limited to states comprising only two photons. In this Letter we propose a scheme for the controlled generation of many entangled photonic qubits. Our source of entanglement produces a train of singlephoton wavepackets which are well resolved in time. This permits us to regard them as individual qubits. In its most simple implementation the setup consists of a single multilevel atom inside an optical resonator [6,7]. The individual wavepackets are generated by applying an external laser pulse to the atom prepared in a superposition state of its internal states. The coupling of the atom to the resonator allows the transfer of a single photon to the resonator and therefrom via cavity decay to the continuum of radiation modes outside the resonator (possibly coupled to an optical fiber). An encoding of quantum information in the one-photon wave-packets could either take place by identifying two orthogonal polarization states of the single photon with logical "0" and "1", or by regarding the absence of a photon as logical "0" while its presence would correspond to logical "1".Our scheme offers a twofold advantage over already existing sources of entangled single-photon wavepackets such as down-conversion. It provides excellent control over the instances in time when a qubit is created as well as over the spectral composition of the wavepacket. The qubits may thus be generated with a well defined tact frequency and pulse shape. Moreover, repeated coherent recycling of the state of the atom after the generation of a photon wave packet gives rise to higher order entanglement between subsequent photons [8]. In this regard our scheme generalizes and extends recent work on sources of single photon wavepackets, commonly referred to as photon guns [9] or turnstile devices [10] by allowing the generation of entangled multiphoton states. In particular, states such as the the three-particle GHZ state, and more generally n-qubit maximally entangled states (MES) can be generat...

We study the physical implementation of an optimal tomographic reconstruction scheme for the case of determining the state of a multi-qubit system, where trapped ions are used for defining qubits. The protocol is based on the use of mutually unbiased measurements and on the physical information described in H. Häffner et. al [Nature 438, 643-646 (2005)]. We introduce the concept of physical complexity for different types of unbiased measurements and analyze their generation in terms of one and two qubit gates for trapped ions.PACS numbers: 03.67. Lx, 03.65.Wj, A main task in any experimental physical setup for implementing quantum computation is the ability to determine the output state of any given quantum algorithm [1]. The standard procedure applied for quantum state reconstruction of a density operator lying in a 2 N dimensional quantum system, in the case of N qubits, consists in projecting the density operator onto 3 N , completely factorized, bases in the corresponding Hilbert space [2]. All these measurements are obtained by applying rotations on single qubits (which are referred to as local operations) followed by projective measurements onto the logical basis. This was recently achieved for the case of eight qubits, with trapped ions [3]. The experiment was done by following the quantum computer architecture based on ions in a linear trap proposed by Cirac and Zoller [4]. Besides, the experimental implementations of several quantum protocols have also been reported by using trapped ions [5]. In all these cases the quality of the protocols is tested using standard tomography for quantum state determination. This scheme has also been used in the cases of considering optical setups [6] and NMR [7].As it was mentioned above, in the standard measurement scheme only local operations are required to generate all the necessary projections. In each basis (setup) 2 N − 1 independent measurements can be performed, so that not all the experimental outcomes obtained in different bases are linearly independent, that is, there are redundant measurements. In the case of a N -qubit system the anti-diagonal elements have the larger errors. Actually, accumulated errors are not uniform; these errors depend on the number of single logic gates used for determining given elements, so that larger errors appear when single logic gates act on all the particles. Assuming that there is an error ε in the measurement of ion populations, then the accumulated error for anti-diagonal elements is of the order of ε 2 N −1 + 2 N −2 (2 N − 1). These errors may lead to a density operator which does not satisfy the positiveness condition and so the information from the experimental data must be optimized. For this purpose the maximum likelihood estimation (MLE) method [8] has been used for the improvement of the density operators in experiments with light qubits [9] as well as in experiments with matter qubits [5].It is well known that the optimal quantum state determination is related to the concept of measurements on Mutually Unbiased Bas...