Scientific Series

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 

I present our work on inferring causality in the classical world and encourage the audience to think about possible generalizations to the quantum world. Statistical dependences between observed quantities X and Y indicate a causal relation, but it is a priori not clear whether X caused Y or Y caused X or there is a common cause of both. It is widely believed that this can only be decided if either one is able to do interventions on the system, or if X and Y are part of a larger set of variables. In the latter case, conditional statistical independences contain some information on causal directions, formalized by the Causal Markov Condition on directed acyclic graphs. Contrary to this belief, we have shown that empirical joint distributions of just two variables often indicate the causal direction. The observed asymmetry between cause and effect is, on the one hand, related to the thermodynamic arrow of time. On the other hand, it can be derived from a new principle that we have postulated: the Algorithmic Causal Markov Condition, which relates Kolmogorov complexity to causality.  
Literature: [1] Janzing, Schoelkopf: Causal inference using the algorithmic Markov condition, IEEE TIT 2010. 
[2] Daniusis, Janzing,...: Inferring deterministic causal relations, UAI 2010. 
[3] Janzing: On the entropy production of time-series with uni-directional linearity.Journ. Stat. Phys. 2010.

During the last ten years, a lot of experimental information has been collected from neutrino oscillation experiments  on the masses and and mixings among the three known  neutrino species. This presents  an almost comparable flavor picture for leptons as is already known to exist for quarks. In the talk I would like to discuss what these results imply for physics beyond the standard model since SM predicts zero neutrino mass. In particular, it seems that one can make a compelling case for the idea of grand unified theory of matter and forces as a candidate theory for neutrinos as well as providing a possible route to flavor unification. I will  outline these arguments,  present a candidate theory and discuss  its tests.

Dwarf galaxies are the most know dark matter dominated luminous objects in Universe. Observing the line of sight velocity and position of stars in Milky way satellites, and assuming the dark matter potential and a specific configuration of stellar orbits, one can obtain the mass profile of dark matter in galaxies. In this talk I will show that by considering a generic case of  phase-space density as a function of energy and angular momentum and by relaxing the specific choice of orbital configuration (which is assumed in literature), we can find  the dark matter potential and mass profile in this general case and restudy the challenges of Cold Dark Matter(CDM) paradigm like core-cusp or missing satellite problem.

We study the problem of reconstructing an unknown matrix M, of rank r and dimension d, using O(rd poly log d) Pauli measurements. This has applications to compressed sensing methods for quantum state tomography.  We give a solution to this problem based on the restricted isometry property (RIP), which improves on previous results using dual certificates. In particular, we show that almost all sets of O(rd log^6 d) Pauli measurements satisfy the rank-r RIP. This implies that M can be recovered from a fixed ("universal") set of Pauli measurements, using nuclear-norm minimization (e.g., the matrix Lasso), with nearly-optimal bounds on the error. Our proof uses Dudley's inequality for Gaussian processes, together with bounds on covering numbers obtained via entropy duality.

The covariant formulation of loop quantum gravity has developed strongly during the last few years.  I summarize the current definition of the theory and the results that have been proven. I discuss what is missing towards of the goal of defining a consistent quantum theory whose classical limit is general relativity.

I will discuss some of the most basic questions in fermionic and bosonic transport, such as the conditions for the existence of a steady-state current, its uniqueness, the role of interactions and spin statistics, its entanglement entropy, etc. This will lead me to introduce an alternative viewpoint to conduction - the micro-canonical formalism of transport - which is ideal to study the above issues [1]. I will point out the similarities and differences with the widely used Landauer formalism, and advance a series of predictions that can be verified by loading ultra-cold atoms into artificial optical lattices.

[1] M. Di Ventra, Electrical Transport in Nanoscale Systems (Cambridge University Press, 2008).

In the de Broglie-Bohm pilot-wave theory, an ensemble of fermions is not only described by a spinor,  but also by a distribution of position beables. If the distribution of positions is different from the one predicted by the Born rule, the ensemble is said to be in quantum non-equilibrium. Such ensembles, which can lead to an experimental discrimination between the pilot-wave theory and standard quantum mechanics, are thought to quickly relax to quantum equilibrium in most cases.   In this talk, I will look at the Majorana equation from the point of view of the pilot-wave theory and I will show that it predicts peculiar trajectories for the beables; they have to move luminally at all times and they usually undergo complex helical trajectories to give the illusion that their motion is subluminal. The nature of the Majorana trajectory suggests that relaxation to quantum equilibrium could only be partial and that quantum non-equilibrium could still survive at length scales below the Compton wavelength.  I investigate this claim, thanks to some numerical simulations of the temporal evolution of non-equilibrium distributions,  for three-dimensional confined systems governed by the Dirac and Majorana equations.