Extending Schmidt vector from pure to mixed states for characterizing entanglement

• Autores: Meroi, F.; Losada, M.; Bosyk, Gustavo Martin
• Año de publicación: 2024
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: ENTANGLEMENT; SCHIMDT VECTOR; MAJORIZATION
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

In this study, we enhance the understanding of entanglement transformations and their quantification by extending the concept of Schmidt vector from pure to mixed bipartite states, exploiting the lattice structure of majorization. The Schmidt vector of a bipartite mixed state is defined using two distinct methods: as a concave roof extension of Schmidt vectors of pure states, or equivalently, from the set of pure states that can be transformed into the mixed state through local operations and classical communication (LOCC). We demonstrate that the Schmidt vector fully characterized separable and maximally entangled states. Furthermore, we prove that the Schmidt vector is monotonic and strongly monotonic under LOCC, giving necessary conditions for conversions between mixed states. Additionally, we extend the definition of the Schmidt rank from pure states to mixed states as the cardinality of the support of the Schmidt vector and show that it is equal to the Schmidt number introduced in previous work [Terhal and Horodecki, Phys. Rev. A 61, 040301(R) (2000)]. Finally, we introduce a family of entanglement monotones by considering concave and symmetric functions applied to the Schmidt vector.
Fil: Meroi, F.. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Losada, M.. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
Fil: Bosyk, Gustavo Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina