Questo sito utilizza cookie di terze parti per inviarti pubblicità in linea con le tue preferenze. Se vuoi saperne di più clicca QUI 
Chiudendo questo banner, scorrendo questa pagina, cliccando su un link o proseguendo la navigazione in altra maniera, acconsenti all'uso dei cookie. OK

Effects of noise in continuous variables quantum communication and measurement

L'anteprima di questa tesi è scaricabile in PDF gratuitamente.
Per scaricare il file PDF è necessario essere iscritto a Tesionline.
L'iscrizione non comporta alcun costo. Mostra/Nascondi contenuto.

4 Chapter 1. Quantum optics for quantum information and communication first theoretical step in this direction is the extension of the projection-valued measures (PVMs), introduced by Von Neumann, to the positive operator-valued measures (POVMs); this is the more general theoretical tool to identify the received state but, as exemplified in Section 1.2.2, could not be always conclusive. Of course the theoretical tool must match a practical implementation of the POVM, so we analyze in detail, in Section 1.3, three different kind measurement, that is photodetection, homodyne detection and heterodyne detection, suitable to gain different pieces of information about the quantum system under investigation. 1.1 The Wigner function In this Section we review some simple formulas that connect the generalized Wigner functions for s-ordering with the density matrix, and vice-versa. These formulas prove very useful for quan- tum mechanical applications as, for example, for connecting Master equations with Fokker-Planck equations, or for evaluating the quantum state from Monte Carlo simulations of Fokker-Planck equations, and finally for studying positivity of the generalized Wigner functions in the complex plane. Since Wigner’s pioneering work [4], generalized phase-space techniques have proved very useful in various branches of physics [5]. As a method to express the density operator in terms of c- number functions, the Wigner functions often lead to considerable simplification of the quantum equations of motion, as for example, for transforming Master equations in operator form into manageable Fokker-Planck differential equations (see, for example, reference [6]). Using the Wigner function one can express quantum-mechanical expectation values in form of averages over the complex plane (the classical phase-space), the Wigner function playing the role of a c-number quasi-probability distribution, which generally can also have negative values. More precisely, the original Wigner function allows to easily evaluate expectations of symmetrically ordered products of the field operators, corresponding to the Weyl’s quantization procedure [7]. However, with a slight change of the original definition, one defines generalized s-ordered Wigner function W s (α, α ∗ ), as follows [8] W s (α, α ∗ )= ∫ C d 2 λ pi 2 e αλ ∗ −α ∗ λ+ 1 2 s|λ| 2 Tr{D(λ)ρ} , (1.1) where α ∗ denotes the complex conjugate of α, the integral is performed on the complex plane with measure d 2 λ = de[λ] dm[λ], ρ being the density operator, and D(α) ≡ exp{αa † −α ∗ a} denotes the displacement operator, where a and a † ([a, a † ] = 1) are the annihilation and creation operators of the field mode of interest, respectively. The Wigner functions in equation (1.1) allow to evaluate s-ordered expectation values of the field operators through the following relation Tr{:(a † ) n a m : s ρ} = ∫ C d 2 αW s (α, α ∗ )α ∗n α m , (1.2) where s is a real number. The particular cases s = −1, 0, 1 correspond to anti-normal, symmetrical, and normal ordering, respectively. In these cases the generalized Wigner function W s (α, α ∗ ) are

Anteprima della Tesi di Andrea Renato Rossi

Anteprima della tesi: Effects of noise in continuous variables quantum communication and measurement, Pagina 5

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.