José Ignacio Burgos (ICMAT, CSIC)
Title: Multiple zeta values and Feynman amplitudes.
Abstract: The basic piece of most quantum field computations are Feynman amplitudes, that are integrals attached to Feynman diagrams. The accurate and fast computation of such integrals is of great importance in theoretical and experimental high energy physics. Many Feynman amplitudes can be interpreted as periods of algebraic varieties. Objects that have been extensively studied by Algebraic Geometers and Number Theorist. For instance low loop order Feynman integrals of a massless phi-4 theory are periods of mixed Tate motives and therefore can be evaluated as multiple zeta values.
In recent years mathematicians and physicist have realized such connection and as a consequence, a wealth of new results and computational techniques have evolved. In this talk I will give a (biased and limited) survey of recent developments in this area.
José Ignacio Latorre (Universitat de Barcelona, associated with MIT in Boston and NUS in Singapur)
Title: Maximal Entanglement.
Abstract: The holographic property of some quantum systems appears to be deeply related to error correction codes and combinatorial design. We present a simple example of such a relation that emerges from maximally entangled quantum states.
Eva Miranda (Universitat Politècnica de Catalunya)
Title: Poisson manifolds of “symplectic” type.
Abstract: In this talk we focus on b^n-symplectic manifolds which
are Poisson manifolds, symplectic away from an hypersurface and which satisfy some transversality conditions. These structures have been studied because of their connections to deformation quantization of manifolds with boundary and have recently proved to be useful as models for some classical systems such as the 3-body problem or integrable systems on manifolds with boundary.
We will introduce some motivating examples and we will present some recent developments which clarify the geometry, topology and dynamics of these manifolds. In particular, we can prove generalizations of classical results in the symplectic realm for these manifolds such as convexity for torus actions or a Delzant theorem but also answer some other questions concerning their dynamics.
Andreas Winter (Universitat Autònoma de Barcelona)
Title: Reading and hiding in quantum systems.
Abstract: Quantum data hiding, originally invented as a limitation on local operations and classical communications (LOCC) in distinguishing globally orthogonal states, is actually a phenomenon arising generically in statistics whenever comparing a ‘strong’ set of measurements (i.e., decision rules) with a ‘weak’ one. The classical statistical analogue of this would be secret sharing, in which two perfectly distinguishable multi-partite hypotheses appear to be indistinguishable when accessing only a marginal. The quantum versions are richer in that for example LOCC allows for state tomography, so the states cannot be come perfectly indistinguishable but only nearly so, and hence the question is one of efficiency. The issues covered in the talk are going to be the following:
1. Every restriction on the allowed measurements, but with arbitrary processing of the measurement data at the end, gives rise to a norm on density matrices, the “distinguishability norm”;we will review the general theory of these [Matthews/Wehner/AW, CMP 291:813-843, 2009].
2. LOCC is perhaps the most natural restriction in multi-partite systems, and we will revisit LOCC data hiding and its efficiency.
3. Gaussian operations and classical computation (GOCC): Not very surprisingly, GOCC cannot distinguish optimally even two coherent states of a single mode [Takeoka & Sasaki, PRA 78:022320, 2008].
But we can find states, each a mixture of multi-mode coherent states, which are almost perfectly distinguishable by suitable measurements, by when restricted to GOCC, i.e. linear optics and postprocessing, the states appear almost identical. The construction is random and relies on coding arguments. Open questions include whether one can give a constructive version of the argument, and whether for instance even thermal states can be used, or how efficient the hiding is.