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Search Results: 1 - 10 of 843 matches for " Damian Markham "
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Entanglement and symmetry in permutation symmetric states
Damian J. H. Markham
Physics , 2010, DOI: 10.1103/PhysRevA.83.042332
Abstract: We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We use the Majorana representation, where these states correspond to points on a sphere. Symmetry of the representation under rotation is equivalent to symmetry of the states under products of local unitaries. The geometric measure of entanglement is thus phrased entirely as a geometric optimisation, and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally we see that different symmetries of the states correspond to different types of entanglement with respect to SLOCC interconvertibility.
Graph States for Quantum Secret Sharing
Damian Markham,Barry C. Sanders
Physics , 2008, DOI: 10.1103/PhysRevA.78.042309
Abstract: We consider three broad classes of quantum secret sharing with and without eavesdropping and show how a graph state formalism unifies otherwise disparate quantum secret sharing models. In addition to the elegant unification provided by graph states, our approach provides a generalization of threshold classical secret sharing via insecure quantum channels beyond the current requirement of 100% collaboration by players to just a simple majority in the case of five players. Another innovation here is the introduction of embedded protocols within a larger graph state that serves as a one-way quantum information processing system.
Local encoding of classical information onto quantum states
Yu Tanaka,Damian Markham,Mio Murao
Physics , 2007,
Abstract: In this article we investigate the possibility of encoding classical information onto multipartite quantum states in the distant laboratory framework. We show that for all states generated by Clifford operation there always exist such an encoding, this includes all stabilizer states such as cluster states and all graph states. We also show encoding for classes of symmetric states (which cannot be generated by Clifford operations). We generalise our approach using group theoretic methods introducing the unifying notion of Pseudo Clifford operations. All states generated by Pseudo Clifford operations are locally encodable (unifying all our examples), and we give a general method for generating sets of many such locally encodable states.
The maximally entangled symmetric state in terms of the geometric measure
Martin Aulbach,Damian Markham,Mio Murao
Physics , 2010, DOI: 10.1088/1367-2630/12/7/073025
Abstract: The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination of analytical and numerical results, the most entangled symmetric states for up to 12 qubits are explored and discussed. The optimization problem on the sphere presented here is then compared with two classical optimization problems on the S^2 sphere, namely Toth's problem and Thomson's problem, and it is observed that, in general, they are different problems.
Thermal robustness of multipartite entanglement of the 1-D spin 1/2 XY model
Yoshifumi Nakata,Damian Markham,Mio Murao
Physics , 2008, DOI: 10.1103/PhysRevA.79.042313
Abstract: We study the robustness of multipartite entanglement of the ground state of the one-dimensional spin 1/2 XY model with a transverse magnetic field in the presence of thermal excitations, by investigating a threshold temperature, below which the thermal state is guaranteed to be entangled. We obtain the threshold temperature based on the geometric measure of entanglement of the ground state. The threshold temperature reflects three characteristic lines in the phase diagram of the correlation function. Our approach reveals a region where multipartite entanglement at zero temperature is high but is thermally fragile, and another region where multipartite entanglement at zero temperature is low but is thermally robust.
Entanglement and local information access for graph states
Damian Markham,Akimasa Miyake,Shashank Virmani
Physics , 2006, DOI: 10.1088/1367-2630/9/6/194
Abstract: We exactly evaluate a number of multipartite entanglement measures for a class of graph states, including d-dimensional cluster states (d = 1,2,3), the Greenberger-Horne-Zeilinger states, and some related mixed states. The entanglement measures that we consider are continuous, `distance from separable states' measures, including the relative entropy, the so-called geometric measure, and robustness of entanglement. We also show that for our class of graph states these entanglement values give an operational interpretation as the maximal number of graph states distinguishable by local operations and classical communication (LOCC), as well as supplying a tight bound on the fixed letter classical capacity under LOCC decoding.
Quantum Secret Sharing with error correction
Aziz Mouzali,Fatiha Merazka,Damian Markham
Computer Science , 2014, DOI: 10.1088/0253-6102/58/5/09
Abstract: We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes always allow error recovery if only one among the sents qubits is disturbed in the transmitting channel. However, if two qubits and more are disturbed, then the correction will depend on the used code.
Information Flow in Secret Sharing Protocols
Elham Kashefi,Damian Markham,Mehdi Mhalla,Simon Perdrix
Electronic Proceedings in Theoretical Computer Science , 2009, DOI: 10.4204/eptcs.9.10
Abstract: The entangled graph states have emerged as an elegant and powerful quantum resource, indeed almost all multiparty protocols can be written in terms of graph states including measurement based quantum computation (MBQC), error correction and secret sharing amongst others. In addition they are at the forefront in terms of implementations. As such they represent an excellent opportunity to move towards integrated protocols involving many of these elements. In this paper we look at expressing and extending graph state secret sharing and MBQC in a common framework and graphical language related to flow. We do so with two main contributions. First we express in entirely graphical terms which set of players can access which information in graph state secret sharing protocols. These succinct graphical descriptions of access allow us to take known results from graph theory to make statements on the generalisation of the previous schemes to present new secret sharing protocols. Second, we give a set of necessary conditions as to when a graph with flow, i.e. capable of performing a class of unitary operations, can be extended to include vertices which can be ignored, pointless measurements, and hence considered as unauthorised players in terms of secret sharing, or error qubits in terms of fault tolerance. This offers a way to extend existing MBQC patterns to secret sharing protocols. Our characterisation of pointless measurements is believed also to be a useful tool for further integrated measurement based schemes, for example in constructing fault tolerant MBQC schemes.
Measurement Based Quantum Computation on Fractal Lattices
Damian Markham,Janet Anders,Michal Hajdu?ek,Vlatko Vedral
Electronic Proceedings in Theoretical Computer Science , 2010, DOI: 10.4204/eptcs.26.10
Abstract: In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.
Quantum secret sharing with qudit graph states
Adrian Keet,Ben Fortescue,Damian Markham,Barry C. Sanders
Physics , 2010, DOI: 10.1103/PhysRevA.82.062315
Abstract: We present a unified formalism for threshold quantum secret sharing using graph states of systems with prime dimension. We construct protocols for three varieties of secret sharing: with classical and quantum secrets shared between parties over both classical and quantum channels.
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