Quadratic Entanglement Criteria for Qutrits

K. Rosołeka, M. Wieśniaka, b, L. Knipsc, d aInstitute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics, and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland bInternational Centre for Theories of Quantum Technologies, University of Gdańsk, Wita Swosza 57, 80-308 Gdańsk, Poland cMax-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany dDepartment für Physik, Ludwig-Maximilians-Universität, D-80797 München, Germany

Received: September 10, 2019; revised version December 2, 2019; in final form December 5, 2019

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The problem of detecting non-classical correlations of states of many qudits is incomparably more involved than in the case of qubits. One reason is that for qubits we have a convenient description of the system by the means of the well-studied correlation tensor allowing to encode the complete information about the state in mean values of dichotomic measurements. The other reason is the more complicated structure of the state space, where, for example, different Schmidt ranks or bound entanglement comes into play. We demonstrate that for three-dimensional quantum subsystems we are able to formulate nonlinear entanglement criteria of the state with existing formalisms. We also point out where the idea for constructing these criteria fails for higher-dimensional systems, which poses well-defined open questions.

DOI:10.12693/APhysPolA.137.374 topics: quantum information, quantum correlations, entanglements, qutrits