Regensburg 2022 – scientific programme

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QI: Fachverband Quanteninformation

QI 9: Quantum Correlations

QI 9.6: Talk

Thursday, September 8, 2022, 10:45–11:00, H8

Hilbert-Schmidt geometry of two-qubit correlations — •Santiago Llorens¹ and Jens Siewert^2,3 — ¹Grup d’Informació Quàntica, Universitat Autònoma de Barcelona, Barcelona, Spain — ²University of the Basque Country and EHU Quantum Center, Bilbao, Spain — ³Ikerbasque, Basque Foundation for Science, Bilbao, Spain

The Bloch representation of quantum states endows the state space with a natural Euclidean geometry via the Hilbert-Schmidt scalar product. Based on this, a Bloch ball-type global view of the state space for a qutrit was found recently. This imposes the question whether an analogous method exists for the simplest quantum correlations – those in a system of two qubits. From such a visualization one may expect a better understanding of the links between the algebraic correlation constraints and their geometric background. We show that indeed the 2-sector (aka as the correlation tensor) of two-qubit states allows for a geometric representation of the algebraic constraints to the entries of the Bloch vector. In this context we provide novel insight into the relation between entanglement quantifiers and characteristic parameters of the Bloch representation of bipartite systems.