Talks

We propose a framework to describe and simulate a class of many-body quantum states. We do so by considering joint eigenspaces of sets of monomial unitary matrices, called "M-spaces"; a unitary matrix is monomial if precisely one entry per row and column is nonzero. We show that M-spaces encompass various important state families, such as all Pauli stabilizer states and codes, the AKLT model, Kitaev's anyon models, W states and several others. We furthermore demonstrate how basic properties of M-spaces can transparently be understood by manipulating their monomial stabilizer groups. Finally we show that a large subclass of M-spaces can be simulated efficiently classically with one unified method. [cf. M. Van den Nest, http://arxiv.org/abs/1108.0531]

As helium-4 is cooled below 2.17 K in undergoes a phase transition to a state of matter known as a superfluid which supports flow without viscosity. This type of dissipationless transport can be observed by forcing helium to travel through a narrow constriction that the normal liquid could not penetrate. Recent advances in nanofabrication techniques allow for the construction of smooth pores with nanometer radii, that approach the truly one dimensional limit. In one dimension, it is believed that a system of bosons (like helium-4) may have startlingly different behavior than in three dimensions. The one dimensional system is predicted to have a linear hydrodynamic description known as Luttinger liquid theory, where no type of long range order can be sustained. In the limit where the pore radius is small,  helium inside the channel would behave as a sort of quasi-supersolid with all correlations decaying as power-laws at zero temperature.  We have performed large scale quantum Monte Carlo simulations of helium-4 inside nanopores of varying radii at low temperatures with realistic helium-helium and helium-pore interactions. The results indicate that helium inside the nanopore forms concentric cylindrical layers surrounding a core that can be fully described via Luttinger liquid theory and provides insights towards the exciting possibility of the experimental detection of a Luttinger liquid.

We establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity. In particular, we establish a direct connection between Mermin-type non-locality scenarios, which we generalise to an arbitrary number of parties, using systems of arbitrary dimension, and performing arbitrary measurements, and a new stronger notion of complementarity which we introduce here.    Our derivation of the fact that strong complementarity is a necessary condition for a Mermin scenario provides a crisp operational interpretation for strong complementarity. We also provide a complete classification of strongly complementary observables for quantum theory, something which has not yet been achieved for ordinary complementarity.  Since our main results are expressed in a diagrammatic language (the one of dagger-compact categories) they can be applied outside of quantum theory, in any setting which supports the purely algebraic notion of strongly complementary observables. We have therefore introduced a method for discussing non-locality in a wide variety of models in addition to quantum theory.    The diagrammatic calculus substantially simplifies (and sometimes even trivialises) many of the derivations, and provides new insights. In particular, the diagrammatic computation of correlations clearly shows how local measurements interact to yield a global overall effect. In other words, we depict non-locality.   This is joint work with Ross Duncan, Aleks Kissinger and Quanlong (Harny) Wang. Paper: arXiv:1203.4988 - LiCS'12