Vladimír Bužek

Quantum secret sharing

Secret sharing is a procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. We show how this procedure can be implemented using Greenberger-Horne-Zeilinger (GHZ) states. In the quantum case the presence of an eavesdropper will introduce errors so that his presence can be detected. We also show how GHZ states can be used to split quantum information into two parts so that both parts are necessary to reconstruct the original qubit.

Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement

A beam splitter is a simple, readily available device which can act to entangle output optical fields. We show that a necessary condition for the fields at the output of the beam splitter to be entangled is that the pure input states exhibit nonclassical behavior. We generalize this proof for arbitrary (pure or impure) Gaussian input states. Specifically, nonclassicality of the input Gaussian fields is a necessary condition for entanglement of the field modes with the help of a beam splitter. We conjecture that this is a general property of beam splitters: Nonclassicality of the inputs is a necessary condition for entangling fields in a beam splitter.

No-Signaling Condition and Quantum Dynamics

We show that the basic dynamical rules of quantum physics can be derived from its static properties and the condition that superluminal communication is forbidden. More precisely, the fact that the dynamics has to be described by linear completely positive maps on density matrices is derived from the following assumptions: (1) physical states are described by rays in a Hilbert space, (2) probabilities for measurement outcomes at any given time are calculated according to the usual trace rule, and (3) superluminal communication is excluded. This result also constrains possible nonlinear modifications of quantum physics.

Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation

We present a general analysis of the role of initial correlations between the open system and an environment on quantum dynamics of the open system.

Dynamics of a two-level atom in a Kerr-like medium

Abstract We consider a generalization of the Jaynes-Cummings model when the cavity is supposed to be filled with a Kerr-like medium. We analyze the dynamics of the system. Namely, we study in detail the collapse-revival phenomenon of the atomic inversion and the inhibited decay of the excited atom. Besides, we describe the squeezing properties of the cavity field and the time evolution of the photon number distribution.

Cold trapped ions as quantum information processors

In this tutorial we review the physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multiple-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on off-resonance transitions associated with a qualitative estimation of the weak-coupling regime is included in Appendix A and of the Lamb-Dicke regime in Appendix B.

Thermalizing Quantum Machines: Dissipation and Entanglement

We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir. We characterize completely the family of thermalizing machines. The model shows a tight link between dissipation, fluctuations, and the maximal entanglement that can be generated by the machines. The interplay of quantum and classical information processes that give rise to practical irreversibility is discussed.

K-Photon Coherent States

Abstract We have introduced an alternative definition of the generalized k-photon coherent states which exhibit kth-order squeezing for k  2.

Generalized coherent state for bosonic realization of SU(2)Lie algebra

We have investigated the statistical properties of fields in the SU(2) generalized coherent state built on the bosonic (Schwinger) representation of the generators of SU(2) Lie algebra. We have shown that there are sub-Poissonian photon statistics as well as anticorrelations. Schemes for the generation of the states under consideration are discussed. We show that in the relevant processes either fields that are highly sub-Poissonian can be generated or a field in one mode with sub-Poissonian statistics can be transformed into another field that also has sub-Poissonian statistics.

Towards quantum-based privacy and voting

The privacy of communicating participants is often of paramount importance, but in some situations it is an essential condition. A typical example is a fair (secret) voting. We analyze in detail communication privacy based on quantum resources, and we propose new quantum protocols. Possible generalizations that would lead to voting schemes are discussed.