Southwest Quantum Information and Technology

Fourteenth Annual Meeting, February 16-19, 2012
Albuquerque, New Mexico

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SESSION 11b: Breakout B - Quantum Information Theory - Alvarado "B"
Session Chair:
4:15pm-4:45pm	Iman Marvian, Perimeter Institute, Institute for quantum computing
	Information-theoretic approach to the study of symmetric dynamics
	Abstract. Information theory provides a novel approach to the study of the consequences of symmetric dynamics which goes far beyond the traditional conservation laws that are derived from Noether's theorem. For one, these conservation laws are not applicable to dissipative and open systems. Moreover, even in the case of closed system dynamics, the conservation laws do not capture all the consequences of symmetry if the state of the system is not pure, as we will show. Using the information theoretic approach to this problem, we introduce new quantities called asymmetry monotones, such that if the system is closed they are constant of the motion and otherwise, if the system is open, they are always non-increasing. We also explain how different results in quantum information theory can have non-trivial consequences about the symmetric dynamics of quantum systems.
4:45pm-5:15pm	Orest Bucicovschi, University of California San Diego
	The achievable values for pairwise concurrences of three qubits
	Abstract. We investigate the set of achievable values for the three pairwise concurrences of a state of three qubits. We show that it is the intersection of the convex hull of the Roman Steiner surface with the positive octant in the space of concurrences, first for X-states, then for any pure state of three qubits. We further show that the allowable set is the solution of a linear matrix inequality involving three other entanglement invariants. We further consider the extension of this result to mixed states and n qubits, n>=3. This is joint work with David A.Meyer and Jon R. Grice
5:15pm-5:45pm	Vlad Gheorghiu, Institute for Quantum Information Sciences and Department of Mathematics and Statistics, Universty of Calgary
	Optimal hybrid quantum secret sharing schemes via stabilizer codes and twirling of symplectic structures
	Abstract. As recently shown in [quant-ph/1108.5541], any quantum error-correcting code can be converted into a perfect "hybrid" quantum secret sharing scheme by allowing the sharing of extra classical bits between the dealer and the players. An advantage of this scheme is that it allows the players' quantum shares to be of smaller dimension than the dimension of the encoded secret, which is impossible for regular perfect quantum secret sharing protocols. Whenever the underlying quantum error correcting code is a stabilizer code (this being the case for the vast majority of known quantum error-correcting codes), I provide a general scheme of reducing the amount of classical communication required, then prove that my scheme is optimal for the stabilizer code being used. The optimality proof is based on the fact that the correlations between the dealer and the players can be fully described by an "information group" [Phys. Rev. A 81, 032326 (2010)]; the symplectic structure of the information group effectively gives the minimum number of classical bits required. Finally I provide an explicit protocol that achieves this minimum by employing the notion of "twirling" (or scrambling) the information group. The results are general and valid for any stabilizer code. I will illustrate the results by simple examples.
5:45pm-6:15pm	Kamil Bradler, School of Computer Science, McGill University
	Crossing Tsirelsons bound with supersymmetric non-local states
	Abstract. We construct a class of supersymmetric entangled states which is used as a nonlocal resource in the CHSH game. If the Grassmann-valued degrees of freedom are accessible to measurement using the proposed measurement model then the entangled state is more nonlocal then a maximally entangled two-qubit state. We show that the winning probability reaches at least pwin=0.8641 which is greater than pwin=cos2(pi/8)=0.8536. This value corresponds to an expected value known as Tsirelsons bound and no ordinary quantum-mechanical entangled state can perform better.