Speaker
Alexander Stottmeister, Leibnitz University of Hanover
Abstract
Quantum information-theoretic results obtained for finite-dimensional systems may fail in systems with an unbounded or infinite number of degrees of freedom. An important example is the failure of uniqueness of purifications in bipartite systems: Two subsystems, described by commuting von Neumann algebras A and B, can be tomographically complete, yet not all purifications of a state on A are connected by unitaries in B. As recently shown, the uniqueness of purifications is equivalent to Haag duality (A = B’). More broadly, this raises the question of which basic entanglement properties survive the transition to infinite-dimensional systems. Here, we show that the possibility to steer any ensemble of the A-marginal of a joint state via measurements on B is equivalent to the existence of a state-preserving conditional expectation from B’ to A. Our results provide a clear connection between the latter and entanglement theory, since conditional expectations are a fundamental concept in operator algebras, particularly in subfactor theory. We also comment on the simple implications for the index of the inclusion of A in B’ in an A-B-symmetric setting. The talk is based on joint work with Lauritz van Luijk, Henrik Wilming, Amine Marrakchi, and Tobias J. Osborne.