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The codification in higher dimensional Hilbert Spaces (whose logical basis states are dubbed qudits in analogy with bidimensional qubits) presents various advantages both for Quantum Information applications and for studies on Foundations of Quantum Mechanics. Purpose of this review is to introduce qudits, to summarize their application to Quantum Communication and researches on Local Realism and, finally, to describe some recent experiment for realizing them. A Little more in details: after a short introduction, we will consider the advantages of testing local realism with qudits, discussing both the 3-4 dimensional case (both for maximally and non-maximally entanglement) and then the extension to an arbitrary dimension. Afterwards, we will discuss the theoretical results on using qudits for quantum communication, epitomizing the outcomes on a larger security in Quantum Key Distribution protocols (again considering separately qutrits, ququats and generalization to arbitrary dimension). Finally, we will present the experiments performed up to now for producing quantum optical qudits and their applications. In particular, we will mention schemes based on interferometric set-ups, orbital angular momentum entanglement and biphoton polarization. Finally, we will summarize what hyperentanglement is and its applications.
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits
Given a protocol ${cal P}$ that implements multipartite quantum channel ${cal E}$ by repeated rounds of local operations and classical communication (LOCC), we construct an alternate LOCC protocol for ${cal E}$ in no more rounds than ${cal P}$ and no
Many beautiful experiments have been addressed to test standard quantum mechanics against local realistic models. Even if a strong evidence favouring standard quantum mechanics is emerged, a conclusive experiment is still lacking, because of low dete
In this paper, we discuss the minimal number of observables, where expectation values at some time instant determine the trajectory of a d-level quantum system (qudit) governed by the Gaussian semigroup. We assume that the macroscopic information abo
(A) Bells theorem rests on a conjunction of three assumptions: realism, locality and ``free will. A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational symmetry o