Abstract: This research-interaction seminar focuses on mathematical aspects of quantum information. In previous semesters we examined various applications of algebra, analysis, and geometry to quantum foundations, quantum cryptography, quantum computing, and other topics in theoretical physics. In this organizational meeting we'll discuss logistics, and then give some short advertisements for papers that we'd like to discuss during the fall semester. Suggestions and contributions are welcome! No previous experience in quantum theory is required, however linear algebra and (discrete) probability is a must. Seminar information is available at http://users.umiacs.umd.edu/~bclackey/QI-RIT2018Fall.html .
Abstract: I will talk about the basics of operational quantum theory, which presents quantum theory as a general probability theory focussing on systems and transformations. The natural language for this formalism is category theory. In this first lecture I will rapidly cover the most basic features of categories, build the framework for describing operational quantum theories, and discuss how these elements are represented in traditional quantum information science.
Abstract: Building on our description of operational quantum theories as categories we will discuss the physical concepts of causality, locality, and purity in the language of symmetric monoidal categories. Finally I will mention a set of additional axioms that singles out traditional quantum mechanics as a generalized probability theory.
Abstract: While diagrams are commonly used as an aid in proofs in quantum information, it is less common to see proofs themselves represented as pictures. Yet, some formal arguments can be more simply represented as pictures rather than equations. Graphical languages for quantum information have been developed (e.g., in the book "Picturing Quantum Processes" by B. Coecke and A. Kissinger) in which every picture-element has a formal meaning. In our work we use formal visual arguments to prove a new result on quantum self-testing: we show that N copies of the GHZ state can be self-tested by three non-communicating parties. I will discuss this proof and give an introduction to diagrammatic quantum information along the way.
Ref: S. Breiner, A. Kalev, C. Miller. "Parallel Self-Testing of the GHZ State with a Proof by Diagrams," https://arxiv.org/abs/1806.04744 .
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