5 M ar 2 00 7 QUANTUM GROUPS ACTING ON 4 POINTS

A ] 3 S ep 2 00 7 QUANTUM GROUPS ACTING ON 4 POINTS

We classify the compact quantum groups acting on 4 points. These are the quantum subgroups of the quantum permutation group Q4. Our main tool is a new presentation for the algebra C(Q4), corresponding to an isomorphism of type Q4 ≃ SO−1(3). The quantum subgroups of Q4 are subject to a McKay type correspondence, that we describe at the level of algebraic invariants.

ar X iv : h ep - t h / 04 08 12 5 v 1 1 7 A ug 2 00 4 Field theoretic models on covariant quantum spaces

ar X iv : 0 70 5 . 07 12 v 1 [ m at h - ph ] 4 M ay 2 00 7 REFLECTION POSITIVITY AND MONOTONICITY

We prove the most general reflection positivity results for both scalar fields and Dirac fields on a Riemannian manifold, and comment on applications to quantum field theory. As another application, we prove the inequality C D ≤ C N between Dirichlet and Neumann covariance operators on a manifold with a reflection.

ar X iv : 0 70 5 . 19 96 v 1 [ qu an t - ph ] 1 4 M ay 2 00 7 Critique of “ Quantum Enigma : Physics encounters Consciousness ”

The central claim that understanding quantum mechanics requires a conscious observer, which is made made by B. Rosenblum and F. Kuttner in their book ”Quantum Enigma: Physics encounters consciousnes”, is shown to be based on various misunderstandings and distortions of the foundations of quantum mechanics.

ua nt - p h / 07 02 07 4 v 4 1 9 M ar 2 00 7 QBC 3 : An Unconditionally Secure Quantum Bit Commitment Protocol

This article describes a quantum bit commitment protocol, QBC3, based on entanglement destruction via forced measurements and proves its unconditional security. Some comments on the current status of the field are also made.