[en] Unitary gates with high entangling power are relevant for several quantum-enhanced technologies due to their entangling capabilities. For symmetric multiqubit systems, such as spin states or bosonic systems, the particle exchange symmetry restricts these gates and also the set of not-entangled states. In this work, we analyze the entangling power of unitary gates in these systems by reformulating it as an inner product between vectors with components given by SU(2) invariants. For small number of qubits, this approach allows us to study analytically the entangling power including the detection of the unitary gate that maximizes it. We observe that extremal unitary gates exhibit entanglement distributions with high rotational symmetry, same that are linked to a convex combination of Husimi functions of certain states. Furthermore, we explore the connection between entangling power and the Schmidt numbers admissible in some quantum state subspaces. Thus, the geometrical approach presented here suggests new paths for studying entangling power linked to other concepts in quantum information theory.
Disciplines :
Physics
Author, co-author :
Serrano Ensástiga, Eduardo ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM)
Morachis Galindo, Diego ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM) ; Departamento de Física, Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de Mexico, Ensenada, Mexico
Maytorena, Jesús A.; Departamento de Física, Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de Mexico, Ensenada, Mexico
Chryssomalakos, Chryssomalis; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de Mexico, Mexico
Language :
English
Title :
Entangling power for symmetric multiqubit systems: A geometrical approach
UNAM - Universidad Nacional Autónoma de México EU - European Union ULiège - University of Liège F.R.S.-FNRS - Fund for Scientific Research
Funding text :
ESE acknowledges support from the postdoctoral fellowship of the IPD-STEMA program of the University of Li\u00E8ge (Belgium) . DMG acknowledges support from the F.R.S.-FNRS under the Excellence of Science (EOS) programme . CC acknowledges support from the UNAM-PAPIIT project IN112224 . JAM and DMG acknowledge support from the UNAM-PAPIIT project IN111122 (M\u00E9xico).
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