Bob Coecke

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Titles and Abstracts of Talks

• Samson Abramsky (40 min): Temperley-Lieb Algebras: from Cut-Elimination to Knot Theory via Quantum Mechanics.
• Dmitri Akatov (15 min): Applications of LQP.
• Thorsten Altenkirch (40 min, joint work with Jonathan Grattage, Amr Sabry and Juliana Vizzotto): Towards a Functional Quantum Programming Language.
• Pablo Arrighi (40 min, joint work with Gilles Dowek): Higher-Order in the Linear-Algebraic Lambda-Calculus.
• Dan Browne (40 min): One-way Quantum Computation in the "Heisenberg Picture". Gottesman and Knill elegantly used the idea of treating the unitary evolution of a qubit register in a quantum computation as an encoding, in what Gottesman called a "Heisenberg picture" of quantum computation, and thus showed the classical simulability of Clifford group networks. In this talk, I will show that a similar approach allows one to understand one-way quantum computation (1WQC) in an elegant way, using a streamlined version [2] of the stabilizer approach to 1WCQ employed by Raussendorf, Briegel and myself in [1]. This approach has a number of appealing features and in particular has produced a few interesting new observations on the 1WQC including a wider class of operations which can be performed in unit time and a simple prescription for the direct design of graph states to implement specific unitary operations. [1] Raussendorf et al, Physical Review A 68 022312, (2003). [2] D.E. Browne, in preparation.
• Bob Coecke (40 min, joint work with Dusko Pavlovic): Quantum measurements as coalgebras (or as pictures, if you prefer). Within the categorical quantum semantics introduced by Abramsky and myself we propose a notion of quantum measurement definable in terms of tensor structure alone, which in the presence of biproducts exactly coincides with projective measurements in terms of mutually orthogonal projectors, as it is the case in Hilbert space quantum mechanics. Its main ingredient are self-adjoint Eilenberg-Moore coalgebras for comonads induced by so-called classical objects, that is, objects equipped with a particular comonoid structure. Via Selinger's CPM-construction, these comonoids also induce decoherence morphisms, which capture the informatic irreversibility of quantum measurement. The comonoid structure also provides a clear categorical analysis of the operations of duplicating and deleting in classical and quantum informatics, and an important corollary to all this this is that quantum measurement, classical data and also decoherence can now be dealt with in purely graphical calculus.
• Ross Duncan (40 min): TBA.
• Chris Heunen (15 min): TBA.
• Peter Hines (40 min): Reversibility and Coherence between Computational Paths.
• Hynek Mlnarik (15 min): Quantum Communication and Programming.
• Nikos Papanikolaou (15 min, joint work with Simon Gay and Rajagopal Nagarajan): Model-Checking Quantum Key Distribution: Techniques and Results. In this talk I will report on recent work on generating finite-state models of quantum protocols for use with the probabilistic model-checker PRISM. I will present some work in progress on developing a tool for generating more substantial models and associated properties for model-checking. I will be referring to some of our earlier work (arXiv: quant-ph/0504007), in which some elementary examples (teleportation, error correction) were described.
• Eric Paquette (40 min, joint work with Bob Coecke): Recasting POVM's in the Category of Completely Positive Maps.
• Simon Perdrix (40 min): Quantum Types for Entanglement and Separability.
• Mehrnoosh Sadrzadeh (15 min): Staying Safe with Bell.
• Sonja Smets (40 min, joint work with Alexandru Baltag): Reasoning about Entanglement: the Logic of Quantum Actions in Compound Systems. I will present the logic LQP, this is a dynamic logic for reasoning about information flow in quantum programs [1]. I will focus in particular on the relational semantics of LQP and on how to characterize by logical means various forms of entanglement. As an example of application, I will use the logic to give a formal proof for the correctness of the Teleportation protocol. [1] A. Baltag and S.Smets, "LQP: The Dynamic Logic of Quantum Information", submitted for publication, [available here]
• Isar Stubbe (15 min): Q-modules are precisely Q-suplattices. It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale (Joyal & Tierney). I shall show a generalization of this result to the case of (ordered) sheaves on a quantaloid.
• Mike Varnava (40 min, joint work with Dan Browne and Terry Rudolph): Linear Optics Quantum Computing Tolerant to Photon Loss. The one-way model for Quantum Computing consists of a special type of entangled resource, known as cluster states (or graph states), and single qubit measurements. These measurements are used to execute the quantum computations while destroying the entanglement in the cluster states. One of the major source of errors in optical implementations of the model is due to photon loss. We have a particular type of cluster state which is tolerant to photon losses. (The main ideas of the implications involved in the functionality will be demonstrated in the talk).