Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues. Contents I

Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement in information processing by a quantum computer. We provide finally some examples of current experimental

It has been recently shown by Mayers that no bit commitment is secure if the participants have unlimited computational power and technology. However it was noticed that a secure protocol could be obtained by forcing the cheater to execute a measurement. Similar situations had been encountered previously in the design of Quantum Oblivious Transfer. The question is whether a classical bit commitment could be used for this specific purpose. We demonstrate that, surprisingly, classical unconditionally concealing bit commitments do not help.

Unconditionally secure two-party bit commitment based solely on the principles of quantum mechanics (without exploiting special relativistic signalling constraints, or principles of general relativity or thermodynamics) has been shown to be impossible, but the claim is repeatedly challenged. The quantum bit commitment theorem is reviewed here and the central conceptual point, that an ``Einstein Podolsky Rosen' ' attack or cheating strategy can always be applied, is clarified. The question of whether following such a cheating strategy can ever be disadvantageous to the cheater is considered and answered in the negative. There is, indeed, no loophole in the theorem. 1.

Abstract. Mayers and independently Lo and Chau have shown that unconditionally secure quantum bit commitment is impossible. In this paper we show that under the assumption that the sender is not able to perform generalized measurements involving more than n qubits coherently (n-coherent measurements) then quantum bit commitment is possible. A commitment scheme is δ-binding if for each execution there is an ˜x ∈{0,1}that cannot be unveiled with probability of success better than δ. Our bit commitment scheme requires the transmission of N qubits and is δ-binding, for any δ>0, if the committer can only carry out n-coherent measurements for some n ∈ Ω(N). For some α> 0, the scheme is 2 −αN-binding against n-coherent measurements for some n ∈ Ω ( √ N). The security against malicious receivers is unconditional. 1

dissertation is the result of my own work and includes nothing which is the outcome Currently, a rethinking of the fundamental properties of quantum mechanical systems in the light of quantum computation and quantum cryptography is taking place. In this PhD thesis, I wish to contribute to this effort with a study of the bipartite quantum state. Bipartite quantum-mechanical systems are made up of just two subsystems, A and B, yet, the quantum states that describe these systems have a rich structure. The focus is two-fold: Part I studies the relations between the spectra of the joint and the reduced states, and in part II, I will analyse the amount of entanglement, or quantum correlations, present in a given state. In part I, the mathematical tools from group theory play an important role, mainly drawing on the representation theory of finite and Lie groups and the Schur-Weyl duality. This duality will be used to derive a one-to-one relation between the spectra of a joint quantum system AB and its parts A and B, and the Kronecker coefficients of the symmetric group. In this way the two problems are connected for the first time, which

The Hughston-Jozsa-Wootters theorem shows that any finite ensemble of quantum states can be prepared “at a distance”, and it has been used to demonstrate the insecurity of all bit commitment protocols based on finite quantum systems without superselection rules. In this paper, we prove a generalized HJW theorem for arbitrary ensembles of states on a C ∗-algebra. We then use this result to demonstrate the insecurity of bit commitment protocols based on infinite quantum systems, and quantum systems with Abelian superselection rules. I.

Unconditionally secure quantum bit commitment has been shown to be impossible by Mayers [22] and Lo and Chau [18, 19], but the claim is repeatedly challenged. The bit commitment theorem is reviewed here and the central conceptual point, that an ”Einstein-Podolsky-Rosen ’ attack or cheating strategy can always be applied, is clarified. The question of whether following such a cheating strategy can ever be disadvantageous to the cheater is considered and answered in the negative. PACS numbers: 03.67.-a, 03.67.Dd, 89.70.+c 1