Generic formula for dynamical entropy of the ball & point quantum system

Anna Szczepanek, Jagiellonian University, Kraków

Joint work with Wojciech Słomczyński

Consider a unitarily evolving 3-dim quantum system (qutrit) that is repeatedly measured with a projective measurement (PVM) consisting of one rank-2 projection and one rank-1 projection. The dynamics of such a system can be visualized as taking place on the union of a Bloch ball and a single point, which correspond to the respective projections.

We investigate the Markov chain that is generically generated on the set of quantum states and employ the Blackwell integral entropy formula in order to derive a closed-form expression for dynamical entropy of this system, thus quantifying the irreducible randomness present in the sequences of emitted measurement outcomes.

Recording of the talk