We study the protocol of qudit teleportation using quantum systems subjected to several kinds of noise for arbitrary dimensionality d. We consider four classes of noise: dit-flip, d-phase-flip, ditphase-flip and depolarizing, each of them corresponding to a family of Weyl operators, introduced via Kraus formalism. We derive a general expression for the average fidelity of teleportation in arbitrary dimension d for any combination of noise on the involved qudits. Under a different approach we derive the average fidelity of teleportation for a more general scenario involving the d-dimensional generalization of amplitude damping noise as well. We show that all possible scenarios may be classified in four different behaviours and discuss the cases in which it is possible to improve the fidelity by increasing the associated noise fractions. All our results are in agreement with previous analysis by Fortes and Rigolin for the case of qubits (Phys. Rev. A, 92 012338, 2015).

We review some current ideas about tripartite entanglement, the case representing the next level of complexity beyond the simplest one (though far from trivial), namely the bipartite. This kind of entanglement has an essential role in the understanding of foundations of quantum mechanics. Also, it allows several applications in the fields of quantum information processing and quantum computing. In this paper, we make a revision about the main foundational aspects of tripartite entanglement and we discuss the possibility of using it as a resource to execute quantum protocols. We present some examples of quantum protocols in detail.

The question of how Bell nonlocality behaves in bipartite systems of higher dimensions is addressed. By employing the probability of violation of local realism under random measurements as the figure of merit, we investigate the nonlocality of entangled qudits with dimensions ranging from d = 2 to d = 7. We proceed in two complementary directions. First, we study the specific Bell scenario defined by the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality. Second, we consider the nonlocality of the same states under a more general perspective, by directly addressing the space of joint probabilities (computing the frequencies of behaviours outside the local polytope). In both approaches we find that the nonlocality decreases as the dimension d grows, but in quite distinct ways. While the drop in the probability of violation is exponential in the CGLMP scenario, it presents, at most, a linear decay in the space of behaviours. Furthermore, in both cases the states that produce maximal numeric violations in the CGLMP inequality present low probabilities of violation in comparison with maximally entangled states, so, no anomaly is observed. Finally, the nonlocality of states with non-maximal Schmidt rank is investigated.

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The problem of noise incidence on qubits taking part of bipartite entanglement-based protocols is addressed. It is shown that the use of a three-partite GHZ state and measurements instead of their EPR counterparts allows the experimenter to detect 2/3 of the times whenever one of the qubits involved in the measurement is affected by bit-flip noise through the mere observation of unexpected outcomes in the teleportation and superdense coding protocols when compared to the ideal case.It is shown that the use of post-selection after the detection of noise leads to an enhancement in the efficiency of the protocols. The idea is extended to any protocol using entangled states and measurements. Furthermore it is provided a generalization in which GHZ states and measurements with an arbitrary amount of qubits are used instead of EPR pairs, and remarkably, it is concluded that the optimal number of qubits is only three.

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Phosphoramidates are common and widespread backbones of a great variety of fine chemicals, pharmaceuticals, additives and natural products. Conventional approaches to their synthesis make use of toxic chlorinated reagents and intermediates, which are sought to be avoided at an industrial scale. Here we report the coupling of phosphites and amines promoted by a Cu3[Co(CN)6]2-based double metal cyanide heterogeneous catalyst using I2 as additive for the synthesis of phosphoramidates. This strategy successfully provides an efficient, environmentally friendly alternative to the synthesis of these valuable compounds in high yields and it is, to the best of our knowledge, the first heterogeneous approach to this protocol. While the detailed study of the catalyst structure and of the metal centers by PXRD, FTIR, EXAFS and XANES revealed changes in their coordination environment, the catalyst maintained its high activity for at least 5 consecutive iterations of the reaction. Preliminary mechanism studies suggest that the reaction proceeds by a continuous change in the oxidation state of the Cu metal, induced by a O2/I− redox cycle.

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