A PHYSICAL DESCRIPTION OF THE SPECTRAL TRANSFORM

A. Boehm

Stergios Pellis

Aloïs Würger

Gilles Brassard A, André Allan Méthot

In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR questioned the completeness of quantum mechanics. The authors argued that the then-new theory should not be considered final because they believed it incapable of describing physical reality. The epic battle between Einstein and Bohr intensified following the latter's response later the same year. Three decades elapsed before John S. Bell gave a devastating proof that the EPR argument was fatally flawed. The modest purpose of our paper is to give a critical analysis of the original EPR paper and point out its logical shortcomings in a way that could have been done 70 years ago, with no need to wait for Bell's theorem. We also present an overview of Bohr's response in the interest of showing how it failed to address the gist of the EPR argument.

ANTHONY CHEFLES, Richard Jozsa, Andreas Winter

Let A={ρ1,…,ρn} be a given set of quantum states. We consider the problem of finding necessary and sufficient conditions on another set B={σ1,…,σn} that guarantee the existence of a physical transformation taking ρi to σi for all i. Uhlmann has given an elegant such condition when both sets comprise pure states. We give a simple proof of this condition and develop some consequences. Then we consider multi-probabilistic transformations between sets of pure states which leads to conditions for the problem of transformability between A and B when one set is pure and the other is arbitrary.