Quantum Cryptography and Entanglement

One of the best known applications of the principles of quantum theory is quantum cryptography, a subject founded by ideas of Wiesner (1983) and Bennett and Brassard (1984). It applies these principles to securely establish a secret key between two distant parties. Quantum cryptography gained public attention after Shor (1994) showed that quantum computers can break most of the cryptographic schemes currently used. Based upon ideas of Ekert (1991), who has shown a relation between quantum cryptography and entanglement purification, it is possible to compute upper and lower bounds on the efficiency of quantum cryptography in various schemes, e.g. ideal or practical qubit and higher-dimensional systems as well as for continuous-variable schemes.

In our group, we currently investigate basic aspects of quantum cryptography and its relation to entanglement:

Quantum cryptography

The peculiar statistical properties of entangled quantum states can be exploited practically for distributing securely private random keys between various parties. Using quantum theory for solving the classically impossible key distribution problem is at the heart of quantum cryptography. The first secure quantum key distribution protocol was propsed in 1984 by Bennett and Brassard (BB84 protocol). In recent years also a thorough theoretical understanding of what the security of such a quantum protocol means has also been obtained. Recently, we analyzed a generalization of the original BB84 protocol which is valid not only for qubits but for arbitrary-dimensional elementary quantum mechanical data carriers and we explored its robustness, i.e. the maximum tolerable error probability which still guarantees the generation of a private random key.

Oliver Kern and Joseph M. Renes, Quantum Information and Computation 8, 756-772 (2008)
J. M. Renes and G. Smith, Phys. Rev. Lett. 98, 020502 (2007)
K. S. Ranade and G. Alber, J. Phys. A 40, 139 (2007)
A. Khalique, Georgios M. Nikolopoulos, and G. Alber, Eur. Phys. J. D (2006)
G. Nikolopoulos, A. Khalique, and G. Alber, Eur. Phys. J. D 37, 441 (2006)
Georgios M. Nikolopoulos, K. S. Ranade, and G. Alber, Phys. Rev. A 73, 032325 (2006)
K.S. Ranade and G. Alber, J. Phys. A 39, 1701 (2006)
G. Nikolopoulos, A. Khalique, and G. Alber, Eur. Phys. J. D 37, 441 (2006)
G. Nikolopoulos and G. Alber, Phys. Rev. A. 72, 032320 (2005)
G. Alber and Th. Walther, Thema Forschung 1, 44 (2004)

Quantum state purification

With the help of nonlinear quantum transformations it is possible to develop purification processes. Typically, in such a purification process one aims at producing a pure entangled quantum state starting from a mixed one by means of local operations only. From the point of view of practical applicability it is desirable to develop purification protocols which are not only efficient but which also involve local operations which can be implemented easily. Such a bipartite purification protocol which purifies arbitrary-dimensional quantum states is developed in

G. Alber, A. Delgado, N. Gisin, and I. Jex, J. Phys. A 34, 8821 (2001).

Contact

Prof. Dr. Gernot Alber

Institut für Angewandte Physik

Hochschulstraße 4a
64289 Darmstadt, Germany

+49-6151/16-20400 (fax: 20402)

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