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topological-entropy
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On the Topological Entropy of Geodesic Flows
, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor) ; Nassiri, Meysam (Supervisor)
Abstract
Let M be a connected, compact, Riemannian manifold. Geodesic flow is a flow on the unit tangent bundle of M . This flow can be studied in dynamics prespective. for example entropy or complexity of the geodesic flow. in this thesis we will follow methods of entropy estimation or computing for geodesic flow. we will follow the method of anthony manning and Ricardo Mañe for proving such result. Maning present two results linking the topological entropy of the geodesic flow on M. we expalin how he find exponential growth rate volume of balls in universal cover as a lower bound for topologycal entropy. another theorem , Mañe represent the equlity between exponential growth rate of avrage of...
Finite-temperature topological order in two-dimensional topological color codes
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 80, Issue 1 , 2009 ; 10502947 (ISSN) ; Sharif University of Technology
2009
Abstract
In this work the topological order at finite temperature in two-dimensional color code is studied. The topological entropy is used to measure the behavior of the topological order. Topological order in color code arises from the colored string-net structures. By imposing the hard constrained limit the exact solution of the entanglement entropy becomes possible. For finite size systems, by raising the temperature, one type of string-net structure is thermalized and the associative topological entropy vanishes. In the thermodynamic limit the underlying topological order is fragile even at very low temperatures. Taking first the thermodynamic limit and then the zero-temperature limit and vice...
Entanglement properties of topological color codes
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 78, Issue 6 , 2008 ; 10502947 (ISSN) ; Sharif University of Technology
2008
Abstract
The entanglement properties of a class of topological stabilizer states, the so-called topological color codes defined on a two-dimensional lattice or 2-colex, are calculated. The topological entropy is used to measure the entanglement of different bipartitions of the 2-colex. The dependency of the ground-state degeneracy on the genus of the surface shows that the color code can support a topological order, and the contribution of the color in its structure makes it interesting to compare with Kitaev's toric code. While a qubit is maximally entangled with the rest of the system, two qubits are no longer entangled showing that the color code is genuinely multipartite entangled. For a convex...