Quantum Foundations

The Wigner-Araki-Yanase (WAY) theorem delineates
circumstances under which a class of quantum measurements is ruled out.
Specifically, it states that any observable (given as a self adjoint operator)
not commuting with an additive conserved quantity of a quantum system and
measuring apparatus combined admits no repeatable measurements. I'll review the
content of this theorem and present some new work which generalises and
strengthens the existing results.

A quantum steering ellipsoid may be used to faithfully represent
a density matrix ? describing two qubits A and B. The ellipsoid is the
geometric set of states that Bob can steer Alice's qubit to when he implements
all possible measurements on his qubit. We show how the correlations between
qubits A and B manifest themselves in this paradigm, giving simple conditions
for when the state is entangled, or has discord. We will also present novel features
of the two qubit state that are revealed by the steering ellipsoid formalism,

The general boundary formulation (GBF) is an atemporal, but spacetime local formulation of quantum theory. Usually it is presented in terms of the amplitude formalism, which, in the presence of a background time, recovers the pure state formalism of the standard formulation of quantum theory. After reviewing the essentials of the amplitude formalism I will introduce a new "positive formalism", which recovers instead a mixed state formalism.