Bounding the Elliptope of Quantum Correlations & Proving Separability in Mixed States
Elie Wolfe Perimeter Institute for Theoretical Physics
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Classical Space Times from S Matrices
Ira Rothstein Carnegie Mellon University
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BiGravity: from Cosmological Solutions to Dual Galileons
Matteo Fasiello University of Portsmouth
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Charged particle motion in magnetized black holes
Valeri Frolov University of Alberta
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Quantum Adversary (Upper) Bound
Shelby Kimmel Massachusetts Institute of Technology (MIT)
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Light and matter: towards macroscopic quantum systems
Jacob Taylor Office of Science and Technology Policy
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The Amplitude Mode in Condensed Matter : Higgs Hunting on a Budget
Daniel Arovas University of California, San Diego
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Topological States in Strongly-Correlated Materials
Kai Sun University of Michigan–Ann Arbor
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N-body lensed CMB maps: lensing extraction and characterization
Claudia Antolini SISSA International School for Advanced Studies
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Bounding the Elliptope of Quantum Correlations & Proving Separability in Mixed States
Elie Wolfe Perimeter Institute for Theoretical Physics
We present a method for determining the maximum possible violation of any linear Bell inequality per quantum mechanics. Essentially this amounts to a constrained optimization problem for an observable’s eigenvalues, but the problem can be reformulated so as to be analytically tractable. This opens the door for an arbitrarily precise characterization of quantum correlations, including allowing for non-random marginal expectation values. Such a characterization is critical when contrasting QM to superficially similar general probabilistic theories. We use such marginal-involving quantum bounds to estimate the volume of all possible quantum statistics in the complete 8-dimensional probability space of the Bell-CHSH scenario, measured relative to both local hidden variable models as well as general no-signaling theories. See arXiv:1106.2169. Time permitting, we’ll also discuss how one might go about trying to prove that a given mixed state is, in fact, not entangled. (The converse problem of certifying non-zero entanglement has received extensive treatment already.) Instead of directly asking if any separable representation exists for the state, we suggest simply checking to see if it “fits” some particular known-separable form. We demonstrate how a surprisingly valuable sufficient separability criterion follows merely from considering a highly-generic separable form. The criterion we generate for diagonally-symmetric mixed states is apparently completely tight, necessary and sufficient. We use integration to quantify the “volume” of states captured by our criterion, and show that it is as large as the volume of states associated with the PPT criterion; this simultaneously proves our criterion to be necessary as well as the PPT criterion to be sufficient, on this family of states. The utility of a sufficient separability criterion is evidenced by categorically rejecting Dicke-model superradiance for entanglement generation schema. See arXiv:1307.5779. -
Classical Space Times from S Matrices
Ira Rothstein Carnegie Mellon University
Progress in calculating S matrix elements have shown that the malicious redundancies in non-linear gauge theories can be circumvented by utilizing unitarity methods in conjunction with BCFW recursion relations. When calculating in this fashion all of the interaction vertices beyond the three point function can be ignored. This simplification is especially useful in gravity which contains an infinite number of such non-linear interactions. It is natural to ask whether off-shell quantities, such as classical solutions, can also be generated using only the three point vertex. In this talk I will show that this is indeed the case by extracting classical solutions to GR from on-hell two to two scattering S-matrix elements. In so doing we will completely circumvent the action as well as the equations of motion. The only inputs will be Lorentz invariance, the existence of a massless spin-two particle and locality. Because of the double copy relation this implies there exists, a yet to be understood, connection between solutions to Yang-Mills theory and Gravity. I will also discuss how this technique can be used to simplify calculations of higher order post-Newtonian corrections to gravitational potentials relevant to the problem of binary inspirals. -
BiGravity: from Cosmological Solutions to Dual Galileons
Matteo Fasiello University of Portsmouth
I will present Cosmological FRW Solutions in BiGravity Theories and discuss their stability. After deriving the stability bound, one realizes that in Bigravity (in contradistinction to the FRW massive gravity case) the tension between requirements stemming from stability and those set by observations is resolved. The stability bound can also be derived in the decoupling limit of Bigravity. In this context an intriguing duality between Galilean interactions has emerged. -
Dimensional reduction in the sky
In several approaches to quantum-gravity, the spectral dimension of spacetime runs from the standard value of 4 in the infrared (IR) to a smaller value in the ultraviolet (UV). Describing this running in terms of deformed dispersion relations, I show that a striking cosmological implication is that that UV behavior leading to 2 spectral dimensions results in an exactly scale-invariant spectrum of vacuum scalar and tensor fluctuations. I discuss scenarios that break exact scale-invariance and show that the tensor to scalar ratio is fixed by the UV ratio between the speed of gravity and the speed of light. Cosmological perturbations in this framework display a wavelength-dependent speed of light, but by transforming to a suitable "rainbow frame" this feature can be removed, at the expense of modifying gravity. In particular it turns out that the following concepts are closely connected: scale-invariance of vacuum fluctuations, conformal invariance of the gravitational coupling, UV reduction to spectral dimension 2 in position space and UV reduction to Hausdorff dimension 2 in energy-momentum space. -
Charged particle motion in magnetized black holes
Valeri Frolov University of Alberta
There exist evidences that magnetic field in the vicinity of astrophysical black holes plays an important role. In particular it is required for explanation of such phenomenon as jet formation. Study of such problems in all their complexity requires 3D numerical simulations of the magnetohydrodynamics in a strong gravitational field. Quite often when dealing with such a complicated problem it is instructive to consider first its simplifications, which can be treated either analytically, or by integrating ordinary differential equations. Motion of a charged particle in a weakly magnetized black hole is an important example. We consider a non-rotating black hole in the weak magnetic field which is homogeneous at infinity. In the talk I discuss the following problems: How does such a magnetic field affect charged particle motion in the equatorial plane? How does it change the radius of the innermost stable circular orbits (ISCO) and period of rotation? I shall demonstratethat the magnetic field increases the efficiency of the energy extraction from the black hole and that magnetized black holes can be used as "particle accelerators". Finally, I shall discuss out-of-equatorial-plane motion and demonstrate that it is chaotic. Possible applications of these results to astrophysics are briefly discussed. -
Quantum Adversary (Upper) Bound
Shelby Kimmel Massachusetts Institute of Technology (MIT)
I discuss a technique - the quantum adversary upper bound - that uses the structure of quantum algorithms to gain insight into the quantum query complexity of Boolean functions. Using this bound, I show that there must exist an algorithm for a certain Boolean formula that uses a constant number of queries. Since the method is non-constructive, it does not give information about the form of the algorithm. After describing the technique and applying it to a class of functions, I will outline quantum algorithms that match the non-constructive bound. -
Light and matter: towards macroscopic quantum systems
Jacob Taylor Office of Science and Technology Policy
Advances in quantum engineering and material science are enabling new approaches for building systems that behave quantum mechanically on long time scales and large length scales. I will discuss how microwave and optical technologies in particular are leading to new domains of many-body physics, both classical and quantum, using photons and phonons as the constituent particles. Furthermore, I will highlight practical consequences of these advances, including improved force and acceleration sensing, efficient signal transduction, and topologically robust photonic circuits. Finally, I will consider how such large quantum systems may help us measure and constrain theories of quantum gravity and gravity-induced decoherence. -
The Amplitude Mode in Condensed Matter : Higgs Hunting on a Budget
Daniel Arovas University of California, San Diego
The amplitude mode is a ubiquitous phenomenon in systems with broken continuous symmetry and effective relativistic dynamics, and has been observed in magnets, charge density waves, cold atom systems, and superconductors. It is a simple analog of the Higgs boson of particle physics. I will discuss the properties of the amplitude mode and its somewhat surprising visibility in two-dimensional systems, recently confirmed in cold atom experiments. The behavior in the vicinity of a quantum critical point will be stressed, comparing theoretical, numerical, and experimental results. -
New Light Species and the CMB - Joint Cosmology/Particle Physics Seminar
The effective number of neutrino species in our universe, Neff, is capable of probing the presence of new light or massless species in our universe. I will first review relevant facts about both CMB measurements of new light species and thermodynamics in the early universe. Then, I will present the effects of many models of BSM physics containing new light species on the CMB, including models containing eV-scale sterile neutrinos compatible with anomalies in neutrino experiments, and interpret the compatibility of the parameter space of these models in terms of the recent results from the Planck satellite. I will argue that the bounds on couplings obtained from the Planck measurement of the CMB are competitive with bounds coming from other areas of physics. -
Topological States in Strongly-Correlated Materials
Kai Sun University of Michigan–Ann Arbor
In the study of strongly-correlated insulators, a long-standing puzzle remained open for over 40 years. Some Kondo insulators (or mixed-valent insulators) display strange electrical transport that cannot be understood if one assumes that it is governed by the three-dimensional bulk. In this talk, I show that some 3D Kondo insulators have the right ingredients to be topological insulators, which we called “topological Kondo insulators”. For a topological Kondo insulator, the low-temperature transport is dominated by the 2D surface rather than the 3D bulk, because the bulk of this material is an insulator while its surface is a topologically-protected 2D metal. This theoretical picture offers a natural explanation for the long-standing puzzle mentioned above. In addition, we also find that Kondo insulators can support another type of nontrivial topological structure protected by lattice symmetries, which we called “topological crystalline Kondo insulators”. In particular, we predict that SmB$_6$ is both a topological Kondo insulator and a topological crystalline Kondo insulator and I will also discuss recent experiments, which reveal the surface states in SmB$_6$. -
N-body lensed CMB maps: lensing extraction and characterization
Claudia Antolini SISSA International School for Advanced Studies
After multiple high precision detections (ACT, SPT, Planck) gravitational lensing has become a new source of relevant cosmological information: combining it with other probes (e.g. the large scale structure) can give significant insight on the evolution of the Dark Energy component. Developing new algorithms of estimate of this signal will allow the community to exploit this observable as a new and independent probe in cosmology. In my talk I will present the reconstruction of the lensing shear pattern and its angular power spectrum from total intensity and polarised CMB maps obtained using Born approximated ray-tracing through N-body simulated structures.The recovered spectra are in agreement with predictions of the underlying ΛCDM with no visible bias, on a scale interval which extends from the arcminute to several degrees over the sky. This demonstrates the feasibility of CMB lensing studies based on large scale simulations of cosmological structure formation in the context of the upcoming large observational campaigns. -
Finite regions, spherical entanglement, and quantum gravity
Hal Haggard Bard College
An exciting frontier in physics is to understand the quantum nature of gravitation in finite regions of spacetime. Study of these regions from ``below'', that is, by studying the quantum geometry of finite regions emerging from loop gravity and spin networks has recently resulted in a new road to the quantization of volume and to evidence that there is a robust gap in the volume spectrum. In this talk I will complement these results with recent work on conformal field theories in a particular finite region, a spherical ball of space. This new view afforded from ``above" gives insights into entanglement and the Reeh-Schlieder theorem, allows calculation of the entanglement spectrum, and suggests a new route to constructing the Minkowski vacuum out of independent finite regions in quantum gravity.