Conference

Quantum Theory can be derived from six operational axioms. We introduce the operational and probabilistic language that is used to formulate the principles. After the basic notions of system, state, effect and transformation are reviewed, the principles are stated, and their immediate consequences and interpretations are analyzed. Finally, some key results that represent milestones of the derivation are discussed, with particular focus on their implications on information processing and their relation with the standard quantum formalism. The global picture of the presentation highlights quantum theory as a particular operational language emerging from a background of information processing theories, thanks to the purification postulate that singles out the strictly quantum features of information.

I provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following: [Axiom 1] Operations correspond to operators. [Axiom 2] Every complete set of positive operators corresponds to a complete set of operations. The following operational postulates are shown to be equivalent to these mathematical axioms: [P1] Definiteness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state. [P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components. [P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components. [P4] Compound permutatability. There exists a compound reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. [P5] Preparability. Filters are non-mixing and non-flattening. Hence, from these postulates we can reconstruct all the usual features of quantum theory: States are represented by positive operators, transformations by completely positive trace non-increasing maps, and effects by positive operators. The Born rule (i.e. the trace rule) for calculating probabilities also follows. See arXiv:1104.2066 for more details. These operational postulates are deeper than those I gave ten years ago in quant-ph/0101012.

Consider the two great physical theories of the twentieth century: relativity and quantum mechanics. Einstein derived relativity from very simple principles. By contrast, the foundation of quantum mechanics is built on a set of rather strange, disjointed and ad hoc axioms, reflecting at best the history that led to discovering this new world order. The purpose of this talk is to argue that a better foundation for quantum mechanics lies within the teachings of quantum information science. The basic postulate is that the truly fundamental laws of Nature concern information, not waves or particles. For example, it is known that quantum key distribution is possible but quantum bit commitment is not and that nature is nonlocal but not as nonlocal as is imposed by causality. But should these statements be considered as theorems or axioms? It's time to pause and reflect on what is really fundamental and what are merely consequences. Could information be the key?

The spin 1/2 Heisenberg model on a triangular lattice with interchain exchange, J', weaker than the intrachain exchange J, is a particularly well-studied frustrated magnet because of its relevance to Cs2CuCl4, which is thought to be in close proximity to a spin liquid phase. Although an incomensurate spiral state is stable for J'~J, a variet of theoretical studies find evidence for spin liquid behavior well before the decoupled chain limit, J'=0, is reached. However, a renormalization group approach found the surprising result that a collinear antiferromagnetic phase was stable for small J'/J. This talk will briefly review earlier studies and present new results on the relative stability of spiral, collinear and spin liquid phases.

Very recently, it has been recognized that excitations out of the ground state of materials known as spin ice can be viewed as magnetic monopoles, the magnetic analog to electric charges. Like electrons and positrons, these particles possess a charge of +Q or -Q and therefore attract or repel each other. Magnetic monopoles, however, can be accelerated using a magnetic field instead of an electric field. In this talk, I will report on experiments deep into the frozen state of the spin ice material holmium titanate where monopoles are few and far between and the material responds very slowly to a changing magnetic field. Taking advantage of the extremely sensitive magnetic field detector known as a superconducting quantum interference device (SQUID), we measure the rate at which the monopoles are created, move about and are eventually annihilated. A surprisingly simple law emerges at low temperatures, known as an Arrhenius law, suggesting that the generation of these magnetic charges requires an energy that does not change in temperature and for a yet unknown reason, is precisely 3 times the energy required to make a single, bare monopole.

Geometrical frustration in magnetic systems provides a rich playground to study the emergence of novel ground states. In systems where not all magnetic couplings can be simultaneously satisfied, conventional long range magnetic order is often precluded, or pushed to much lower emperature scales than would be expected from the strength of the magnetic interactions. Dy2Ti2O7 has a pyrochlore lattice, where the magnetic Dy ions lie on the vertices of corner sharing tetrahedra. The Dy magnetic moments are constrained by crystal fields to lie along local <111> axes, pointing towards or away from the tetrahedral centres. With a ferromagnetic interaction between nearest neighbours, the ground state for each tetrahedron has two spins pointing in and two out. Due to the number of possible ways of satisfying this constraint, the overall ground state is highly degenerate; in fact this system can be mapped onto the problem of water ice where each oxygen atom has two strongly bound and two weakly bound protons, leading the magnetic problem to be referred to as spin ice. Recent theoretical work in understanding the magnetic excitation in spin ice, where the spin flip excitations can be described in terms of magnetic monopoles. Bramwell et al., reported muon spin rotation measurements of spin ice which they interpreted in terms of this monopole picture. In contrast to the work of Bramwell et al., our muon spin relaxation measurements do not exhibit highly temperature dependent Arrhenius processes expected for monopoles. Instead we report temperature independent spin fluctuations well into the spin ice state and that the previous interpretations are incorrect.

Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the ν=0, ±1, ±2, ±3, ±4 quantum Hall states in bilayer graphene is analyzed. In particular, in the undoped graphene, corresponding to the ν =0 state, two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane (Δ0,B), where Δ0 is a top-bottom gates voltage imbalance, is described. It is shown that the energy gaps in these phases scale linearly, ΔE~10 B [T] K, with magnetic field. The ground states of the doped states, with ν=±1, ±2, ±3, ±4, are also described. The comparison of these results with recent experiments in bilayer graphene is presented.

The nature of the pairing mechanism in the recently discoverediron-pnictide family of superconductors remains an outstanding issue. To answer this question, it is instructive to know the symmetry of the superconducting energy gap. Low temperature thermal conductivity measurements provide a robust test of the presence or absence of low energy electronic quasiparticles that in turn can be used to characterise the symmetry of the gap function. In this talk, I will review what has been learnt so far from such measurements across several families of iron-pnictide superconductors, including our own recent results on the stoichiometric material LaFePO.

Direct visualization of the electronic structure within each crystalline unit cell of a solid is a new frontier in condensed matter physics (M.J. Lawler et al, Nature 466, 347 (2010)). In this talk, I will introduce the techniques of spectroscopic imaging scanning tunneling microscopy (SI-­‐STM) and then explain how our new application of this technique allows visualization of the intra-­‐unit-­‐cell electronic structure. We use this approach to study the pseudogap phase of cuprate high temperature superconductors. Recent experiments provide evidence that this phase may be associated with spontaneously broken electronic symmetries. By studying the Bragg peaks in Fourier transforms of SI-­-STM images, and in particular by resolving both the real and imaginary components of these Bragg amplitudes (as opposed to the Bragg intensities without phase information which are the observables in scattering experiments), we reveal the intra-­‐unit-­‐cell broken electronic symmetries of the cuprate pseudogap phase (J.P.Hinton et al, Science (2011)).

Recently resonant elastic soft x-ray scattering (RSXS) has emerged as a powerful new tool to study electronic ordering in materials like cuprates and manganites. The power of this technique is to combine xray scattering, which is sensitive to spatial order, with x-ray spectroscopy, which is sensitive to the valence, spin and orbital symmetry of specific atoms. This combination allows one to probe very directly and considerable detail a variety of exotic spin, charge, orbital or structural ordering phenomena. I will discuss the application of this technique to an investigation of charge density wave (CDW) order in the cuprate superconductor La1.475Nd0.4Sr0.125CuO4. Analysis of the photon energy dependence of the resonant scattering intensity provides unique insight into the microscopic details of the CDW ordering. New results from the REIXS beamline at the Canadian Light Source will be presented.