University of New Mexico
Talks by Howard Barnum
TBA
Howard Barnum
University of New Mexico
Entropy, majorization, and thermodynamics in general probabilistic theories.
Howard Barnum
University of New Mexico
Much progress has recently been made on the finegrained thermodynamics and statistical mechanics of microscopic physical systems, by conceiving of thermodynamics as a resource theory: one which governs which transitions between states are possible using specified "thermodynamic" (e.g. adiabatic or isothermal) means. In this talk we lay some groundwork for investigating thermodynamics in generalized probabilistic theories.
Generalizations of Quantum Theory

Lucien Hardy Perimeter Institute for Theoretical Physics

Rafael Sorkin Perimeter Institute for Theoretical Physics

Wayne Myrvold Western University

Howard Barnum University of New Mexico

Joe Henson Evince Asset Management LP

Markus Mueller Institute for Quantum Optics and Quantum Information (IQOQI)  Vienna
Composite systems and information processing
Howard Barnum
University of New Mexico
The talk will focus primarily on recent work with Alexander Wilce in which we show that any locally tomographic composite of a qubit with any finitedimensional homogeneous selfdual (equivalently Jordanalgebraic) system must be a standard finitedimensional quantum (i.e. $C^*$algebraic) system. I may touch on work in progress with collaborators on composites of arbitrary homogeneous selfdual systems.
Probabilities from Quantum States, or Quantum States from Probabilities?
Howard Barnum
University of New Mexico
I will consider various attempts to derive the quantum probabilities from the HIlbert space formalism within the manyworlds interpretation, and argue that they either fail, or depend on tacit probabilistic assumptions. The main problem with the project is that it is difficult to understand what the state of system X is psi even *means* without already supposing some probabilistic link to definite observed or observable phenomena involving X.
Jordan algebras and spectrality as tools for axiomatic characterization
Howard Barnum
University of New Mexico
The normalizedstate spaces of finitedimensional Jordan algebras constitute a relatively narrow class of convex sets that includes the finitedimensional quantum mechanical and classical state spaces. Several beautiful mathematical characterizations of Jordan statespaces exist, notably Koecher's characterization as the bases of homogeneous selfdual cones, and Alfsen and Shultz's characterization based on the notion of spectral convex sets plus additional axioms.
Convex and Categorial Frameworks for Information Processing and Physics
Howard Barnum
University of New Mexico
TBA
SICs, Convex Cones, and Algebraic Sets
Howard Barnum
University of New Mexico
The question whether SICs exist can be viewed as a question about the structure of the convex set of quantum measurements, or turned into one about quantum states, asserting that they must have a high degree of symmetry. I\'ll address Chris Fuchs\' contrast of a \'probability first\' view of the issue with a \'generalized probabilistic theories\' view of it. I\'ll review some of what\'s known about the structure of convex state and measurement spaces with symmetries of a similar flavor, including the quantum one, and speculate on connections to recent SIC triple product results.
Information Processing in Convex Operational Theories: Toward a characterization of quantum mechanics
Howard Barnum
University of New Mexico
The rise of quantum information science has been paralleled by the development of a vigorous research program aimed at obtaining an informational characterization or reconstruction of the quantum formalism, in a broad framework for stochastic theories that encompasses quantum and classical theory, but also a wide variety of other theories that can serve as foils to them.
Nonlocal nosignalling correlations that are locally quantum.
Howard Barnum
University of New Mexico