Entanglement measures

Uyanık, Kıvanç
Being a puzzling feature of quantum mechanics, entanglement caused many debates since the infancy days of quantum theory. But it is the last two decades that it has started to be seen as a resource for physical tasks which are not possible or extremely infeasible to be done classically. Popular examples are quantum cryptography - secure communication based on laws of physics - and quantum computation - an exponential speedup for factoring large integers. On the other hand, with current technological restrictions it seems to be difficult to preserve specific entangled states and to distribute them among distant parties. Therefore a precise measurement of quantum entanglement is necessary. In this thesis, common bipartite and multipartite entanglement measures in the literature are reviewed. Mathematical definitions, proofs of satisfaction of basic axioms and significant properties for each are given as far as possible. For Tangle and Geometric Measure of Entanglement, which is a multipartite measure, results of numerical calculations for some specific states are shown.


Entanglement transformations
Kıntaş, Seçkin; Turgut, Sadi; Department of Physics (2009)
Entanglement is a special correlation of the quantum states of two or more particles. It is also a useful resource enabling us to complete tasks that cannot be done by classical means. As a result, the transformation of entangled states of distant particles by local means arose as an important problem in quantum information theory. In this thesis, we first review some of the studies done on the entanglement transformations. We also develop the necessary and sufficient conditions for the deterministic transf...
İnvestigating the semileptonic B to K1(1270,1400) decays in QCD sum rules
Dağ, Hüseyin; Zeyrek, Mehmet Tevfik; Department of Physics (2010)
Quantum Chromodynamics(QCD) is part of the Standard Model(SM) that describes the interaction of fundamental particles. In QCD, due to the fact that strong coupling constant is large at low energies, perturbative approaches do not work. For this reason, non-perturbative approaches have to be used for studying the properties of hadrons. Among several non-perturbative approaches, QCD sum rules is one of the reliable methods which is applied to understand the properties of hadrons and their interactions.\ In th...
Entanglement in the relativistic quantum mechanics
Yakaboylu, Enderalp; İpekoğlu, Yusuf; Department of Physics (2010)
In this thesis, entanglement under fully relativistic settings are discussed. The thesis starts with a brief review of the relativistic quantum mechanics. In order to describe the effects of Lorentz transformations on the entangled states, quantum mechanics and special relativity are merged by construction of the unitary irreducible representations of Poincaré group on the infinite dimensional Hilbert space of state vectors. In this framework, the issue of finding the unitary irreducible representations of ...
Gödel Spacetime
Kavuk, Mehmet; Sarıoğlu, Bahtiyar Özgür; Department of Physics (2005)
In this thesis properties of the Gödel spacetime are analyzed and it is explicitly shown that there exist closed timelike curves in this spacetime. Geodesic motions for massive particles and light rays are investigated. One observes the focusing effect as a result of the solution of the geodesic equations. The time it takes for a free particle released from a point to come back to its starting point is calculated. A geometrical interpretation of the Gödel spacetime is given and the question of what the Göde...
Black hole collisions at the speed of light
Şentürk, Çetin; Karasu, Atalay; Department of Physics (2010)
The main purpose of this work is to study the collision of two black holes and the energy loss due to the gravitational waves emitted during this collision in the framework of general relativity. For this purpose we first study plane wave geometries and their collisions. More realistic collisions are the pp-wave collisions. As an analytic treatment of this problem, we investigate the head-on collision of two ultra-relativistic black holes. Treating the problem perturbatively, we extract the news function to...
Citation Formats
K. Uyanık, “Entanglement measures,” M.S. - Master of Science, Middle East Technical University, 2008.