Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session V7: Randomness and Chaos in Quantum Information Processing |
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Sponsoring Units: DAMOP Chair: C. Stephen Hellberg, NRL Room: LACC 408B |
Thursday, March 24, 2005 11:15AM - 11:51AM |
V7.00001: Random subspaces in quantum information theory Invited Speaker: The selection of random unitary transformations plays a role in quantum information theory analogous to the role of random hash functions in classical information theory. Recent applications have included protocols achieving the quantum channel capacity and methods for extending superdense coding from bits to qubits. In addition, the corresponding random subspaces have proved useful for studying the structure of bipartite and multipartite entanglement. In quantum information theory, we're fond of saying that Hilbert space is a big place, the implication being that there's room for the unexpected to occur. The goal of this talk is to further bolster this homespun wisdowm. I'm going to present a number of results in quantum information theory that stem from the initially counterintuitive geometry of high-dimensional vector spaces, where subspaces with highly extremal properties are the norm rather than the exception. Peter Shor has shown, for example, that randomly selected subspaces can be used to send quantum information through a noisy quantum channel at the highest possible rate, that is, the quantum channel capacity. More recently, Debbie Leung, Andreas Winter and I demonstrated that a randomly chosen subspace of a bipartite quantum system will likely contain nothing but nearly maximally entangled states, even if the subspace is nearly as large as the original system in qubit terms. This observation has implications for communication, especially superdense coding. [Preview Abstract] |
Thursday, March 24, 2005 11:51AM - 12:27PM |
V7.00002: Exploring Dynamical Localization on a Quantum Information Processor Invited Speaker: An experiment which investigates dynamical localization in an implementation of the quantum sawtooth map is presented. In the appropriate parameter regimes, the quantum sawtooth map produces localized states which have a characteristic localization length. This unique quantum behavior, which we observe in a nuclear magnetic resonance quantum information processor, can be used to assess the accuracy of control achieved in a quantum computation device. Measurement of the predicted localization length provides a quantitative measure of experimental control of quantum coherence. [Preview Abstract] |
Thursday, March 24, 2005 12:27PM - 1:03PM |
V7.00003: Simulation of Quantum Chaotic Phenomenas on a Quantum Computer Invited Speaker: The ability of a quantum computer to simulate quantum chaotic phenomena is shown to be more powerful than a classical computer. Specifically, the effects of localization, hypersensitivity to perturbation and entanglement evolution are explored. [Preview Abstract] |
Thursday, March 24, 2005 1:03PM - 1:39PM |
V7.00004: Pseudo-Random Operators for Quantum Information Processing: Theory and Applications Invited Speaker: I will review some important applications of random operators for quantum communication tasks and then describe the usefulness of random operators for efficiently characterizing noise sources and the degree of coherent control present on a quantum processing device. Since the exact implementation of random unitary operators is infeasible in practice on a large quantum processor, I will describe a random circuit method for generating pseudo-random unitary operators and clarify the relationship between these pseudo-random operators and (uniformly) random operators. I will also describe a recent implementation of pseudo-random unitary operators on an scalable NMR quantum processor in which the pseudo-random operators were applied to efficiently simulate a complex dynamical environment and study the generic features of decoherence resulting from different system-environment couplings. [Preview Abstract] |
Thursday, March 24, 2005 1:39PM - 2:15PM |
V7.00005: Entanglement Generation of Not-Quite-Random Marices Invited Speaker: We investigate the connections between randomness and entanglement by exploring the entanglement generation of operators that have certain properties approaching those of random matrices. Certain random matrix statistical properties are shown to affect the entanglement generation and, by idnetifying operators which can fulfill these statistical properties we attempt to formulate what possibly efficient ways to achieve a random state on a quantum computer. [Preview Abstract] |
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