COMPLETE POSITIVITY AND THE NEUTRAL KAON SYSTEM

Abstract. New experiments on neutral K-mesons might turn out to be promising tests of the hypothesis of Complete Positivity in the physics of open quantum systems. In particular, a consistent dynamical description of correlated neutral kaons seems to ask for Complete Positivity. 1. Introduction. Quantum dynamical semigroups provide a useful framework for the description of quite a variety of quantum open systems (S) ([1, 2]). From a general point of view, the latter are considered as subsystems interacting with a suitable environment (E). If the coupling between S and E is sufficiently weak, the effective evolution of S is expected to be irreversible and free from complicated feed-back and memory effects. Under these hypothesis, via weak-coupling limits techniques, one can indeed deduce an effective Markoffian dynamics ([1-4]). That is, the space of states ρ (density matrices) of S is transformed into itself by a one-parameter family γ t : ρ → γ t [ρ] of linear maps satisfying γ s • γ t = γ t+s for s, t ≥ 0 and preserving the positivity of any initial state ρ. However, it turns out that the dynamical maps γ t obtained in this way enjoy the stronger property of being completely positive ([5, 6]). That is, they remain positive when naturally extended from linear transformations on the state-space of S to linear transformations on the state-space of the system S coupled with any finite-level system E n of arbitrary dimension n