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Effects of noise in continuous variables quantum communication and measurement

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Chapter 1 Quantum optics for quantum information and communication In quantum information and communication, a set of quantum states ρ i is used to encode the information and then is sent toward the receiver through a quantum noisy channel. In the fol- lowing we will always assume that the ρ i ’s are chosen between the states of the electromagnetic field. There are a number of reasons for this. First of all, photons are easily produced, both in coherent and incoherent beams, by lasers and thermal sources while, exploiting the properties of nonlinear crystals, it is possible to achieve the production of entangled photons, thus solving the problem of having the entangled resource needed to perform the tasks outlined in the introduction. Second, photons are easily manipulated: beam splitters, high reflectivity mirrors and rotating wave plates are well within today’s technology reach. The third, and most important property, is that photons does not interact among themselves, so that we are guaranteed that, if we produce a state with defined characteristics, and manipulate it in a carefully unitary way, it will retain all of its properties, as long as it propagates in a not too “aggressive” environment. The last requirement, moreover, is usually quite well satisfied in the optical region because, in standard conditions, the average number of thermal photons is very small. In this Chapter we give a review of the mathematical methods and detection schemes used in quantum optics. We review the notion of Wigner function, i.e. the map between the operators used to describe quantum object, and the set of quasi-probability functions on the complex plane. This map is of fundamental importance to reduce the almost always unmanageable operator equations, needed to study the evolution of a system coupled to an environment, to more amenable partial differential equations, that usually take the form of a Fokker-Planck equation. As stated in the introduction, the possibility for Bob to precisely measure a received quantum state, is fundamental to establish reliable quantum communication channels. This is due to the fact that the set of quantum states used by Alice to encode the information to be sent, need not to be necessarily a set of orthogonal states and, even if they are, the interaction with the environment, though possibly reduced to a minimum, can destroy their orthogonality. From this fact arises the need for Bob, to discriminate in a reliable way between the states he gets. A 3

Anteprima della Tesi di Andrea Renato Rossi

Anteprima della tesi: Effects of noise in continuous variables quantum communication and measurement, Pagina 4

Tesi di Dottorato

Dipartimento: Fisica

Autore: Andrea Renato Rossi Contatta »

Composta da 108 pagine.

 

Questa tesi ha raggiunto 360 click dal 21/04/2005.

Disponibile in PDF, la consultazione è esclusivamente in formato digitale.