SAMOP 2023 – scientific programme
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QI: Fachverband Quanteninformation
QI 11: Quantum Entanglement I
QI 11.7: Talk
Tuesday, March 7, 2023, 12:45–13:00, B305
Geometry of the state space of two qubits — •Simon Morelli1, Christopher Eltschka2, Marcus Huber3, and Jens Siewert4,5 — 1Basque Center for Applied Mathematics (BCAM), 48009 Bilbao, Spain — 2Istitut für Theoretische Physik, Universität Regensburg, 93053 Regensburg, Germany — 3Atominstitut, Technische Universität Wien, 1020 Vienna, Austria — 4University of the Basque Country UPV/EHU, 48080 Bilbao, Spain — 5IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
The quantum marginal problem and related questions have received considerable attention recently. We investigate an even simpler question for which there is no answer so far: Given the purities of the two local states of a bipartite system, what is the maximum purity the global state can achieve? We derive an exact solution for two qubits. Together with previous findings [1], this result gives rise for a new representation of the state space – the Bloch ball – of two qubits. We show that this visualization has various interesting properties regarding geometry, majorization, and entanglement.
[1] S. Morelli, C. Kloeckl, C. Eltschka, J. Siewert, and M. Huber,
Lin. Alg. App. 584, 294 (2020).