This paper provides a technical description of the SuperNova Early Warning System (SNEWS), an international network of experiments with the goal of providing an early warning of a galactic supernova.
Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott's code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.
Abstract. We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, "Unperformed experiments have no results." The tools of quantum information theory, and in particular the symmetric informationally complete (SIC) measurements, provide a concise expression of how exactly Peres's dictum holds true. That expression is a constraint on how the probability distributions for outcomes of different, hypothetical and mutually exclusive experiments ought to mesh together, a type of constraint not foreseen in classical thinking. Taking this as our foundational principle, we show how to reconstruct the formalism of quantum theory in finite-dimensional Hilbert spaces. The central variety of mathematical entity in our reconstruction is the qplex, a very particular type of subset of a probability simplex. Along the way, by closely studying the symmetry properties of qplexes, we derive a condition for the existence of a d-dimensional SIC.
This article situates QBism among other well-known interpretations of quantum mechanics. QBism has its roots in personalist Bayesian probability theory, is crucially dependent upon the tools of quantum information, and in latest developments has set out to investigate whether the physical world might be of a type sketched in the philosophies of pragmatism, pluralism, nonreductionism, and meliorism. Beyond conceptual issues, the technical side of QBism is focused on the mathematically hard problem of finding a good representation of quantum mechanics purely in terms of probabilities, without amplitudes or Hilbert-space operators. The best candidate representation involves an entity called a symmetric informationally complete quantum measurement, or SIC. Contemplation of it gives a way to think of the Born rule as an addition to the rules of probability theory, applicable when an agent considers gambling on the consequences of her actions on the external world, duly taking into account a new universal capacity: namely, Hilbert-space dimension. The article ends by showing that the egocentric elements in QBism represent no impediment to pursuing quantum cosmology and even open up possibilities never dreamt of in the usual formulations.
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