Freiburg 2019 – wissenschaftliches Programm
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FM: Fall Meeting
FM 20: Entanglement: Many-Body States II
FM 20.5: Talk
Montag, 23. September 2019, 17:30–17:45, 2004
Shareability of USp⊗USp symmetric states — •Zoltán Zimborás1, Michael Keyl2, Thomas Schulte-Herbrüggen3, and Robert Zeier3,4 — 1Wigner Research Centre for Physics, H-1021 Budapest, Hungary — 2Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany — 3Technical University Munich, Department of Chemistry, Lichtenbergstrasse 4, 85747 Garching, Germany — 4Forschungszentrum Jülich GmbH, Peter Grünberg Institute, Quantum Control (PGI-8), 54245 Jülich, Germany
It is notoriously hard to calculate entanglement measures for generic quantum states. Therefore, from the beginning of entanglement theory it has been useful to consider examples of entangled states with high symmetry, since representation theoretic methods can then be used to greatly simplify the computations of the measures and the characterization of entanglement properties. In the present work, we continue this program by studying states that are invariant with respect to USp(2n)⊗USp(2n) transformations. This symmetry defines a two-parameter family of states in any 2n × 2n dimensional bipartite Hilbert-space. The two free parameters are related by partial transposition in much the same way as isotropic and Werner states, but unlike those states the studied family also contains a region with bound entangled states. Using group theoretical methods, we calculate the one-distillability and two- and three-shareability regions for this set of states, and discuss how these relate to mean-field many-body problems.