Georgios M. Nikolopoulos

Fundamental quantum optics in structured reservoirs

We review basic quantum electrodynamics and quantum optics aspects in microstructures that exhibit a gap in the spectrum of the electromagnetic radiation they support, known as photonic crystals. After a brief sketch of the properties of such materials we discuss the behaviour of few-level atoms or collections thereof with transition frequencies inside and in the vicinity of the gap. The discussion is cast in terms of a unified formalism which facilitates the comparison with standard cavity-atom physics.

Applications of single-qubit rotations in quantum public-key cryptography

We discuss cryptographic applications of single-qubit rotations from the perspective of trapdoor one-way functions and public-key encryption. In particular, we present an asymmetric cryptosystem whose security relies on fundamental principles of quantum physics. A quantum public key is used for the encryption of messages while decryption is possible by means of a classical private key only. The trapdoor one-way function underlying the proposed cryptosystem maps integer numbers to quantum states of a qubit and its inversion can be infeasible by virtue of the Holevos theorem.

Quantum State Transfer and Network Engineering

Faithful communication is a necessary precondition for large-scale quantum information processing and networking, irrespective of the physical platform. Thus, the problems of quantum-state transfer and quantum-network engineering have attracted enormous interest over the last years, and constitute one of the most active areas of research in quantum information processing. The present volume introduces the reader to fundamental concepts and various aspects of this exciting research area, including links to other related areas and problems. The implementation of state-transfer schemes and the engineering of quantum networks are discussed in the framework of various quantum optical and condensed matter systems, emphasizing the interdisciplinary character of the research area. Each chapter is a review of theoretical or experimental achievements on a particular topic, written by leading scientists in the field. The volume aims at both newcomers as well as experienced researchers.

Beyond single-photon localization at the edge of a photonic band gap

We study spontaneous emission in an atomic ladder system, with both transitions coupled near resonantly to the edge of a photonic band gap continuum. The problem is solved through a recently developed technique and leads to the formation of a two-photon

Faithful communication Hamiltonian in photonic lattices

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Perfect state transfer in networks of arbitrary topology and coupling configuration

atom bound state with fractional population trapping in both upper states. In the long-time limit, the atom can be found excited in a superposition of the upper states and a direct two-photon process coexists with the stepwise one. The sensitivity of the effect to the particular form of the density of states is also explored.

Error tolerance of two-basis quantum key-distribution protocols using qudits and two-way classical communication

Faithful communication is a necessary precondition for large scale all-optical networking and quantum information processing. Related theoretical investigations in different areas of physics have led to various proposals in which finite discrete lattices are used as channels for short-distance communication tasks. Here, in the framework of femtosecond-laser-written waveguide arrays, we present the first experimental realization of such a channel with judiciously engineered couplings.

Security bound of two-basis quantum-key-distribution protocols using qudits

A general formalism of the problem of perfect state transfer is presented. We show that there are infinitely many Hamiltonians that may provide a solution to this problem. In a first attempt to give a classification of them we investigate their possible forms and the related dynamics during the transfer. Finally, we show how the present formalism can be used for the engineering of perfect quantum wires of various topologies and coupling configurations.

State transfer in static and dynamic spin chains with disorder

We investigate the error tolerance of quantum cryptographic protocols using d-level systems. In particular, we focus on prepare-and-measure schemes that use two mutually unbiased bases and a key-distillation procedure with two-way classical communication. For arbitrary quantum channels, we obtain a sufficient condition for secret-key distillation which, in the case of isotropic quantum channels, yields an analytic expression for the maximally tolerable error rate of the cryptographic protocols under consideration. The difference between the tolerable error rate and its theoretical upper bound tends slowly to zero for sufficiently large dimensions of the information carriers.

Deterministic quantum-public-key encryption: Forward search attack and randomization

We investigate the security bounds of quantum-cryptographic protocols using d-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the Bennett-Brassard 1984 quantum-key-distribution scheme to higher dimensions. Under the assumption of general coherent attacks, we derive an analytic expression for the ultimate upper security bound of such quantum-cryptography schemes. This bound is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions such an equivalence is generally no longer valid.