Trace-scaling automorphisms of certain stable AF algebras

Trace scaling automorphisms of stable AF algebras with dimension group totally ordered are outer conjugate if the scaling factors are the same (not equal to one). This is an adaptation of a similar result for the AFD type II_infty factor by Connes and extends the previous result for stable UHF algebras.Comment: 12 pages, late

Optimal Measurements for Tests of EPR-Steering with No Detection Loophole using Two-Qubit Werner States

It has been shown in earlier works that the vertices of Platonic solids are good measurement choices for tests of EPR-steering using isotropically entangled pairs of qubits. Such measurements are regularly spaced, and measurement diversity is a good feature for making EPR-steering inequalities easier to violate in the presence of experimental imperfections. However, such measurements are provably suboptimal. Here, we develop a method for devising optimal strategies for tests of EPR-steering, in the sense of being most robust to mixture and inefficiency (while still closing the detection loophole of course), for a given number $n$ of measurement settings. We allow for arbitrary measurement directions, and arbitrary weightings of the outcomes in the EPR-steering inequality. This is a difficult optimization problem for large $n$, so we also consider more practical ways of constructing near-optimal EPR-steering inequalities in this limit.Comment: 15 pages, 11 Figure

On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues

A virial theorem is established for the operator proposed by Brown and Ravenhall as a model for relativistic one-electron atoms. As a consequence, it is proved that the operator has no eigenvalues greater than $\max(m c^2, 2 \alpha Z - \frac{1}{2})$, where $\alpha$ is the fine structure constant, for all values of the nuclear charge $Z$ below the critical value $Z_c$: in particular there are no eigenvalues embedded in the essential spectrum when $Z \leq 3/4 \alpha$. Implications for the operators in the partial wave decomposition are also described.Comment: To appear in Letters in Math. Physic