演講訊息 TALKS

Abstract Let [image: \Phi] be a bijection (not assumed affine nor continuous) from the normal state space of one quantum system, modelled on the self-adjoint part of a von Neumann algebra [image: M_1], to that of another one, modelled on another von Neumann algebra [image: M_2].As a ``generalising'' of Wigner's theorem, we show that there exists a Jordan [image: ^*]-isomorphism [image: \Theta:M_2\to M_1] with[image: \Phi =\Theta_*|_{\mathbb S(M_1)}] if and only if [image: \Phi] preserves a notion of ``asymmetric transition probabilities''. If [image: \Phi] is assumed to preserve either the Raggio or the Uhlmann transition probabilities instead, then [image: M_1] and [image: M_2] are Jordan [image: *]-isomorphic.On the other hand, in the spirit of Uhlhorn's theorem, we show that if [image: \Phi] is biorthogonality preserving, i.e. zero transition probability preserving, then [image: M_1] and [image: M_2] are Jordan [image: ^*]-isomorphic. As an application, we show that the sets of normal states equipped with some metrics are complete Jordan invariants for the underlying von Neumann algebras.