title: Quantum theory with bold operator tensors.
abstract: In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to quantum field theory.
authors.affiliation: Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5 lhardy@pitp.ca.
authors.forename: Lucien
authors.initials: L
authors.lastname: Hardy
keywords: operational physics; operator tensors; quantum theory