Simon J. D. Phoenix

Periodicity, phase, and entropy in models of two-photonresonance

The excitation of Rydberg atom transitions by submillimeter-wavelength radiation in high-Q cavities forms the basis of the micromaser. The excitation dynamics of a micromaser is known to be dependent on the detailed photon statistics in the interaction cavity and can exhibit well-known collapses and revivals of the atomic inversion, dipole moment, and photon number. We study these effects in a two-photon model in which the time evolution is exactly periodic. We study the field entropy in two two-photon cases and link the fluctuations in the field phase to the changes in the field entropy. We also calculate the statistical Q function of the field and show how the periodicity of the two-photon dynamics is linked to a periodic splitting of the Q function in phase space. Finally this periodicity is linked to the nature of the atom-field dressed states involved in two-photon resonance.

Multi-user Quantum Cryptography on Optical Networks

Abstract Quantum cryptography has been shown to be an effective technology for the secure distribution of keys on point-to-point optical links. We show how the existing techniques can be extended to allow multi-user secure key distribution on optical networks. We demonstrate that using network configurations typical of those found in passive optical network architectures any of the current quantum key distribution protocols can be adapted to implement secure key distribution from any user to any other user. An important feature of these adapted protocols is that the broadcaster, or service provider on the network, does not have to be trusted by the two users who wish to establish a key.

Quantum cryptography: How to beat the code breakers using quantum mechanics

Abstract In a series of recent experiments a radical new technique has been demonstrated that could have far-reaching consequences for the way in which the confidentiality and integrity of our networks is protected. This technique, known as quantum cryptography, is the result of a synthesis of ideas from fundamental quantum physics and classical encryption and has lead to a radical new approach to the business of secure communications. We review the origins of and developments in this rapidly growing field and assess the current status of both the theory and the experiments.

Non-local Interatomic Correlations in the Micromaser

Abstract The interaction of an atom with the intracavity field of a micromaser will, in general leave the atom-field system in an entangled state. The long cavity lifetime means that the memory of this entanglement can persist and influence the interaction with subsequent atoms. We show how non-local correlations between successive atoms can be induced leading to a violation of Bells inequality.

Eavesdropping Strategies and Rejected-data Protocols in Quantum Cryptography

Abstract We show that rejected-data protocols for quantum cryptography are secure against generalized intercept/resend strategies of an eavesdropper provided that the legitimate users of the communication channel use at least three bases. We discuss the connection between this result and the recently-developed protocol based on violations of a suitably-constructed Bell-type inequality for single particles. We also give a new estimate of the probability that an eavesdropper remains undetected under the original protocol and thereby show that the optimal strategies available to an eavesdropper are further limited to those which randomize the errors between the sub-ensembles of data. This result also has implications for the way in which the legitimate users of the channel choose their test data.

Three-state quantum cryptography

Abstract We introduce a protocol for quantum key distribution using three mutually non-orthogonal states. The protocol generates key bits most efficiently for three symmetric states. The generalized measurements which minimize the error probability and maximize the mutual information for such a system are known and can be implemented optically. We analyse eavesdropping strategies based on these optimal measurements.

Cryptography, trusted third parties and escrow

The promise of tomorrows electronic business environment will not be fully realised unless government, business and consumers have a high level of confidence in the security of that environment. The use of cryptography can provide this confidence and facilitate the establishment of a global electronic market-place. Cryptographic techniques offer a range of services including confidentiality, authenticity, integrity and anonymity. We examine some of these techniques and explain why a trusted third party infrastructure is seen as a crucial component in the successful introduction of an electronic business arena. The widespread use of cryptography, however, also presents possible new opportunities for criminal activity. To mitigate against this many governments have proposed the provision of escrowed cryptographic services — we review a particular scheme favoured by the UK government.

Counter-rotating Contributions in the Jaynes-Cummings Model

Abstract We present several perturbative approaches to the Jaynes-Cummings model of optical resonance with the counter-rotating terms included. We find that there exists a hitherto overlooked phase-dependence of the atomic inversion which is due to an interference between the rotating wave and counter-rotating contributions.

The soliton phase

Abstract We have made a detailed study of the soliton phase which has been successfully used to predict the properties of a number of soliton based devices. We show how the concept can be generalised to an arbitrary number of solitons.

Mini-maximizing two qubit quantum computations

Two qubit quantum computations are viewed as two player, strictly competitive games and a game-theoretic measure of optimality of these computations is developed. To this end, the geometry of Hilbert space of quantum computations is used to establish the equivalence of game-theoretic solution concepts of Nash equilibrium and mini-max outcomes in games of this type, and quantum mechanisms are designed for realizing these mini-max outcomes.