5 papers
How to unitarily map between any two pure states with a single closed-form exponential
Peter T. J. Bradshaw, Marcus Gouveia, Jonte R. Hance
It is well-known that any two pure quantum states (in the same Hilbert space) can be mapped to any other using unitary transformations. However, previous approaches to this problem…
A Relationship Between Spin and Geometry
Peter T. J. Bradshaw
In a recent paper, algebraic descriptions for all non-relativistic spins were derived by elementary means directly from the Lie algebra $\specialorthogonalliealgebra{3}$, and a con…
An Algebraic Theory of Non-Relativistic Spin
Peter T. J. Bradshaw
In this paper we present a new, elementary derivation of non-relativistic spin using exclusively real algebraic methods. To do this, we formulate a novel method to decompose the do…
Growth in Sumsets of Higher Convex Functions
Peter J. Bradshaw
The main results of this paper concern growth in sums of a -convex function . Firstly, we streamline the proof of a growth result for where has small additive doub…
Higher Convexity and Iterated Second Moment Estimates
Peter J. Bradshaw, Brandon Hanson, Misha Rudnev
We prove bounds for the number of solutions to over -element sets of reals, which are sufficiently convex or near-convex. A near-conv…