Experimental Study of the Quantum States of Light and Realization of a Quantum Communication Protocol\ud

I present how to obtain and characterize quantum states of light potentially useful for quantum communication protocols. The control of the frequency correlations,\ud and the bandwidth, of single and paired photons is an essential ingredient in specific quantum applications, from quantum imaging to quantum clock synchronization.\ud I show both theoretical and experimental spectral correlations of pairs of photons generated in non-collinear spontaneous parametric down conversion (SPDC). In the second part of the work, a scheme for quantum key distribution using the two-way LM05 protocol [PRL 94, 140501 (2005)] and its implementation is presented too. A preliminary transmission test is discussed together with\ud an experimental study for the security of the generated key in presence of noise in the channels. The noise is modulated as to simulate the effect of an eavesdropper.\u

Quantum versus classical domains for teleportation with continuous variables

By considering the utilization of a classical channel without quantum entanglement, fidelity Fclassical=1/2 has been established as setting the boundary between classical and quantum domains in the teleportation of coherent states of the electromagnetic field [S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, J. Mod. Opt. 47, 267 (2000)]. We further examine the quantum-classical boundary by investigating questions of entanglement and Bell-inequality violations for the Einstein-Podolsky-Rosen states relevant to continuous variable teleportation. The threshold fidelity for employing entanglement as a quantum resource in teleportation of coherent states is again found to be Fclassical=1/2. Likewise, violations of local realism onset at this same threshold, with the added requirement of overall efficiency η>2/3 in the unconditional case. By contrast, recently proposed criteria adapted from the literature on quantum-nondemolition detection are shown to be largely unrelated to the questions of entanglement and Bell-inequality violations

From "Dirac combs" to Fourier-positivity

Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its tensor products in higher dimensions lead to Poisson resummation, allowing for a useful approximation formula of a Fourier transform in terms of a limited number of terms. A connection with the Bochner theorem on positive definiteness of Fourier-positive functions is discussed. As a practical application, we find simple and rapid analytic algorithms for checking Fourier-positivity in 1- and (radial) 2-dimensions among a large variety of real positive functions. This may provide a step towards a classification of positive positive-definite functions.Comment: 17 pages, 14 eps figures (overall 8 figures in the text

The String Tension in Gauge Theories

A review article on string tension concept and their relevance as non-perturbative quantity on the study of quark confinement in lattice gauge theories. A detailed description of a variety of methods to measure the string tension on the lattice and an indication of the most promising developments is proposed.Comment: Postscript file, 46 pages and 14 figure

Assumptions in Quantum Cryptography

Quantum cryptography uses techniques and ideas from physics and computer science. The combination of these ideas makes the security proofs of quantum cryptography a complicated task. To prove that a quantum-cryptography protocol is secure, assumptions are made about the protocol and its devices. If these assumptions are not justified in an implementation then an eavesdropper may break the security of the protocol. Therefore, security is crucially dependent on which assumptions are made and how justified the assumptions are in an implementation of the protocol. This thesis is primarily a review that analyzes and clarifies the connection between the security proofs of quantum-cryptography protocols and their experimental implementations. In particular, we focus on quantum key distribution: the task of distributing a secret random key between two parties. We provide a comprehensive introduction to several concepts: quantum mechanics using the density operator formalism, quantum cryptography, and quantum key distribution. We define security for quantum key distribution and outline several mathematical techniques that can either be used to prove security or simplify security proofs. In addition, we analyze the assumptions made in quantum cryptography and how they may or may not be justified in implementations. Along with the review, we propose a framework that decomposes quantum-key-distribution protocols and their assumptions into several classes. Protocol classes can be used to clarify which proof techniques apply to which kinds of protocols. Assumption classes can be used to specify which assumptions are justified in implementations and which could be exploited by an eavesdropper. Two contributions of the author are discussed: the security proofs of two two-way quantum-key-distribution protocols and an intuitive proof of the data-processing inequality.Comment: PhD Thesis, 221 page

Event program

UNLV Undergraduates from all departments, programs and colleges participated in a campus-wide symposium on April 16, 2011. Undergraduate posters from all disciplines and also oral presentations of research activities, readings and other creative endeavors were exhibited throughout the festival