Thomas Durt

Quantum nonlocality in two three-level systems

Recently a new Bell inequality has been introduced (CGLMP,KKCZO) that is strongly resistant to noise for maximally entangled states of two d-dimensional quantum systems. We prove that a larger violation, or equivalently a stronger resistance to noise, is found for a non-maximally entangled state. It is shown that the resistance to noise is not a good measure of non-locality and we introduce some other possible measures. The non-maximally entangled state turns out to be more robust also for these alternative measures. From these results it follows that two Von Neumann measurements per party may be not optimal for detecting non-locality. For d=3,4, we point out some connections between this inequality and distillability. Indeed, we demonstrate that any state violating it, with the optimal Von Neumann settings, is distillable.

Security of Quantum Key Distribution with entangled Qutrits.

The study of quantum cryptography and quantum entanglement have traditionally been based on two-level quantum systems (qubits). In this paper, we consider a generalization of Ekerts entanglement-based quantum cryptographic protocol where qubits are replaced by three-level systems (qutrits). In order to investigate the security against the optimal individual attack, we derive the information gained by a potential eavesdropper applying a cloning-based attack. We exhibit the explicit form of this cloner, which is distinct from the previously known cloners, and conclude that the protocol is more robust than those based on entangled qubits as well as unentangled qutrits.

Quantum, classical and intermediate: An illustrative example

We present a model that allows one to build structures that evolve continuously from classical to quantum, and we study the intermediate situations, giving rise to structures that are neither classical nor quantum. We construct the closure structure corresponding to the collection of eigenstate sets of these intermediate situations, and demonstrate how the superposition principle disappears during the transition from quantum to classical. We investigate the validity of the axioms of quantum mechanics for the intermediate situations.

Experimental Quantum Cloning with Prior Partial Information

When prior partial information about a state to be cloned is available, it can be cloned with a fidelity higher than that of universal quantum cloning. We experimentally verify this intriguing relationship between the cloning fidelity and the prior information by reporting the first experimental optimal quantum state-dependent cloner, using nuclear magnetic resonance techniques. Our experiments may further cast important implications into many quantum information processing protocols.

Security of quantum key distributions with entangled qudits

We consider a generalization of Ekerts entanglement-based quantum cryptographic protocol where qubits are replaced by N- or d-dimensional systems (qudits). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerfs formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of qudit generalizations of the Ekerts protocol for qubits.

About mutually unbiased bases in even and odd prime power dimensions

Mutually unbiased bases generalize the X, Y and Z qubit bases. They possess numerous applications in quantum information science. It is well known that in prime power dimensions N = pm (with p prime and m a positive integer), there exists a maximal set of N + 1 mutually unbiased bases. In the present paper, we derive an explicit expression for those bases, in terms of the (operations of the) associated finite field (Galois division ring) of N elements. This expression is shown to be equivalent to the expressions previously obtained by Ivanovic (1981 J. Phys. A: Math. Gen. 14 3241) in odd prime dimensions, and Wootters and Fields (1989 Ann. Phys. 191 363) in odd prime power dimensions. In even prime power dimensions, we derive a new explicit expression for the mutually unbiased bases. The new ingredients of our approach are, basically, the following: we provide a simple expression of the generalized Pauli group in terms of the additive characters of the field, and we derive an exact groupal composition law between the elements of the commuting subsets of the generalized Pauli group, renormalized by a well-chosen phase-factor.

A Model with Varying Fluctuations in the Measurement Context

In the “hidden measurement formalism,” we try to explain the emergence of the quantum probabilities from the presence of fluctuations in the measurement context. We use a model that was constructed by Aerts et al. as a metaphorical model to extend these ideas.

Quantum Structures in Macroscopic Reality

We show that it is possible to construct macroscopic entities that entail a quantum logical structure. We do this by means of the introduction of a simple macroscopic entity and study its structure in terms of lattices and graphs, and show that the lattice is non-Boolean.

Violations of local realism with quantum systems described byN-dimensional Hilbert spaces up toN=16

Predictions for systems in entangled states cannot be described in local realistic terms. However, after admixing some noise such a description is possible. We show that for two quNits (quantum systems described by N dimensional Hilbert spaces) in a maximally entangled state the minimal admixture of noise increases monotonically with N. The results are a direct extension of those of Kaszlikowski et. al., Phys. Rev. Lett. {\bf 85}, 4418 (2000), where results for

Cloning a qutrit

N\leq 9