Security of quantum key distribution with entangled qutrits

Abstract

We consider a generalisation of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by quN its (i.e., N -dimensional systems). 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 Cerf's 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 quN it generalisations of the Ekert's protocol for qubits.PACS numbers: 03.65. Ud.03.67.Dd.89.70.+c Recently it was shown that this violation is more pronounced for the case of entangled quNits [3,4,5] for N > 2. Moreover, the qutrit generalisation of Ekert's protocol is more robust

Robustness of a quantum key distribution with two and three mutually unbiased bases

“…The cases with two and four bases are studied analytically in [7], while in [10,11] the case with three mutually unbiased bases is studied numerically. The results obtained both with the most general unitary eavesdropping strategy and with the optimal quantum cloning machine are exactly the same.…”

“…In these sections we find the optimal eavesdropping strategy and we compare the results with those ones obtained by an optimal quantum cloning machine. The generalization to four-dimensional systems and the comparison with the corresponding results derived from cloning attacks [7,10,11] is discussed in Sec. III, in a protocol with only two unbiased bases.…”

Stationary State Entanglement and Total Correlation of Two Qubits or Qutrits

“…Quantum communication complexity protocol with two entangled qutrits has been proposed [8], and it has been proven that, for a broad class of protocols the entangled state of two qutrits can enhance the efficiency of solving the problem in the quantum protocol over any classical one if and only if the state violates Bell's inequality for two qutrits. By making use of the entangled qutrits, a generalization of Ekert's entanglement-based quantum cryptographic protocol has been discussed [9]. By means of the orbital angular momentum of the photons, the experimental implementation of producing, transmitting, and reconstructing the qutrit has been reported [10].…”

Quantum Information Processing by Nmr: Preparation of Pseudopure States and Implementation of Unitary Operations in a Single-Qutrit System

“…The degree of non-local correlations are in fact greater in case of entangled qutrits (three-level systems) than entangled qubits [8]. Several cryptographic protocols have been devised using qutrits which are argued to be highly secure against symmetric attacks [9][10][11]. Recently it has also been demonstrated that qutrits can be useful for certain purposes of quantum simulation [12], quantum computations [13][14][15] and quantum communication [16][17][18][19].…”