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Q: Fachverband Quantenoptik und Photonik
Q 39: Posters: Quantum Optics and Photonics III
Q 39.52: Poster
Mittwoch, 11. März 2020, 16:30–18:30, Empore Lichthof
Monte Carlo simulations for determining the volume ratio separable to entangled states in a two-qubit system — •Héctor José Moreno1, Jósef Zsolt Bernád1,2, and Gernot Alber1 — 1Institut für Angewandte Physik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany — 2Department of Physics, University of Malta, Msida MSD 2080, Malta
In this work, we investigate the question of how many separable states are in the set of all quantum states. We focus on a two-qubit composite system and its Fano type of parametrization. The number of free parameters is 15 and due to the chosen parametrization, we are able to characterize general self-adjoint matrices with trace one and eigenvalues between minus one and one. Thus, the first task is to find all positive matrices, i.e., the density matrices, which can be realized with the help of the Newton identities. These identities lead to three inequalities and these analytical results are investigated with the help of Monte Carlo simulations. Then, the separability of the states is determined using the Peres-Horodecki criterion. While many previous approaches have considered this question, here we try a different numerical and analytical approach for estimating the volume ratio of separable to entangled states. Our combined analytical and numerical approaches can also be extended to a qubit- qutrit system, where the Peres-Horodecki criterion still holds.