Scientific Series

Two-party Bell correlation inequalities (that is, inequalities involving only correlations between dichotomic observables at each site, such as the CHSH inequality) are well-understood: Grothendieck's inequality stipulates that the quantum bias can only be a constant factor larger than the classical bias, and the maximally entangled state is always the most nonlocal resource. In part due to the complex nature of multipartite entanglement, tripartite inequalities are much more unwieldy. In a recent breakthrough result, Perez-Garcia et. al. (quant-ph/0702189) showed using tools originating from the study of operator algebras that in this setting the quantum-classical violation could be arbitrarily large. Moreover, they showed that GHZ states could only lead to bounded violations, so that they were not the most non-local states. We extend and simplify their results in a number of ways: - We show that large families of states, including generalizations of GHZ states and stabilizer states, can only lead to bounded violations. - We prove bounds on the maximal quantum-classical violation as a function both of the local dimension (this was already shown in Perez-Garcia et. al., but we give a much simpler proof), and of the number of settings per site. - We provide a simple probabilistic construction of an inequality for which there is an unbounded quantum-classical gap. Our construction is simpler, and has better parameters, than the one in Perez-Garcia et.al. It is essentially optimal in terms of the local dimension of one of the parties, and off by a quadratic factor in terms of the number of settings. In this talk I will survey some of these results, focusing on the tools that have so far been useful for their analysis (and do not involve operator algebras!). Based on joint works with Jop Briet, Harry Buhrman, and Troy Lee. Some of this work is available at arXiv:0911.4007.

At the time of recombination, 400,000 years after the Big Bang, the structure of the dark matter distribution was extremely simple and can be inferred directly from observations of structure in the cosmic microwave background. At this time dark matter particles had small thermal velocities and their distribution deviated from uniformity only through a gaussian field of small density fluctuations with associated motions. Later evolution was driven purely by gravity and so obeyed the collisionless Boltzmann equation. This has immediate consequences for the present distribution of dark matter, even in extremely nonlinear regions such as the part of the Galaxy where the Sun resides. I will show how this structure can be followed in full generality by integrating the Geodesic Deviation Equation in tandem with the equations of motion in a high-resolution N-body simulation, enhancing its effective resolution by more than 10 orders of magnitude. I will discuss how the predicted distribution at the Sun's position impacts the expectations for laboratory experiments seeking to detect the dark matter directly, in particular, the possibility of extremely narrow line signals that may be visible in axion detectors.

We will discuss the effect of non-equilibrium drive near a quantum critical point in itinerant electron systems. Non-equilibrium field theory is formulated in terms of the Keldysh functional integral. The renormalization group approach is used to study the universality class of the non-equilibrium phase transition in the steady state system. The role of the non-equilibrium drive in the quantum-classical crossover will be discussed using the example of the Hertz-Millis theory and the generalization thereof.

On small scales the cosmic microwave background (CMB) is perturbed by large scale structure in the universe, primarily through Compton scattering and gravitational lensing. The current generation of CMB experiments is measuring these signals, allowing new measurements of the build-up of cosmic structure. I will discuss two such measurements being made with the South Pole Telescope: 1) through Compton scattering (the Sunyaev-Zeldovich effect) we have compiled a large catalog of very massive galaxy clusters extending to z>1, allowing a measure of the growth of structure from z=1 to today; 2) we are currently measuring the gravitational lensing of the CMB, providing an accurate measure of the integrated structure between z=0 and z=1100. Both of these are powerful new tests of our cosmological understanding.

Many fundamental results in quantum foundations and quantum information theory can be framed in terms of information-theoretic tasks that are provably (im)possible in quantum mechanics but not in classical mechanics. For example, Bell's theorem, the no-cloning and no-broadcasting theorems, quantum key distribution and quantum teleportation can all naturally be described in this way. More generally, quantum cryptography, quantum communication and quantum computing all rely on intrinsically quantum information-theoretic advantages. Much less attention has been paid to the information-theoretic power of relativistic quantum theory, although it appears to describe nature better than quantum mechanics. This talk describes some simple information-theoretic tasks that distinguish relativistic quantum theory from quantum mechanics and relativistic classical physics, and a general framework for defining tasks that includes all previously known (im)possibility theorems and raises many open questions. This suggests a new way of thinking about relativistic quantum theory, and a possible new approach to defining non-trivial relativistic quantum theories rigorously. I also describe some simple and surprisingly powerful applications of these ideas to cryptography, including a new secure scheme for simultaneously committing to and encrypting a prediction and ways of securely "tagging" an inaccessible object so as to guarantee its position.

The local and global properties of the retarded and Feynman Green functions to the wave equation in curved spacetime are crucial for radiation reaction in the classical theory and for renormalisation in the quantum quantum theory. Building on an insight due to Avramidi, we provide a system of transport equations for determining key fundamental geometrical bitensors determining the local Hadamard singularity structure of these Green’s functions. We illustrate their use in a semi-recursive approach showing how to determine covariant expansions to high order, for example, calculating the tail term reflecting backscattering by the curvature of spacetime to 20th order in the geodesic separation in a matter of minutes, and as the basis of numerical calculations. We also present an efficient method to construct covariant expansions of the tail term, without using the formal Hadamard light-cone expansion. Finally we discuss the relationship between the geodesic structure, quasi-normal modes with associated excitation factors and the global behaviour of Green functions in black hole space-times.

We propose a mechanism where high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites useful for quantum computation and multi-party quantum communication. We observe that the key features of the entanglement dynamics of the composite spin chain are remarkably well described using a simple model of two singlets, each formed by two spins. The proposed entanglement routing mechanism is a footprint of the emergence of a Kondo cloud in a Kondo system and can be engineered and observed in varied physical settings.

In the last many years a number of metallic solids have been studied that defy understanding within the principles of conventional textbook solid state physics. The most famous are the cuprate high temperature superconductors though many other examples have been found. In this talk I will argue that the mysterious properties of many such materials arises from an imminent `death' of their Fermi surfaces. I will discuss some theoretical ideas on how to kill a Fermi surface, and their implications for experiments.

Usually, quantum theory (QT) is introduced by giving a list of abstract mathematical postulates, including the Hilbert space formalism and the Born rule. Even though the result is mathematically sound and in perfect agreement with experiment, there remains the question of why this formalism is a natural choice, and how QT could possibly be modified in a consistent way. My talk is on recent work with Lluis Masanes, where we show that five simple operational axioms actually determine the formalism of QT uniquely. This is based to a large extent on Lucien Hardy's seminal work. We start with the framework of "general probabilistic theories", a simple, minimal mathematical description for outcome probabilities of measurements. Then, we use group theory and convex geometry to show that the state space of a bit must be a 3D (Bloch) ball, finally recovering the Hilbert space formalism. There will also be some speculation on how to find natural post-quantum theories by dropping one of the axioms.