Día: Viernes 20 de enero
Hora: 11:00
Lugar: Sala de seminarios de l Seminario de Física Atómica. Tercera Planta de Físicas. Facultad de Ciencias.
Conferenciante: Prof. Adan Cabello. Universidad de Sevilla.
Resumen:
For years, the statement that quantum mechanics exhibits state-independent contextuality (SIC) has been based on a mathematical result pointed out by Kochen and Specker (KS) and Bell: the existence of the so-called KS sets. Recently, Yu and Oh (arXiv:1109.4396) have observed that KS sets are not necessary to prove SIC. Here we show that a set of observables in dimension d represented by rank-1 projectors reveals SIC if and only if the graph in which vertices represent vectors and edges link orthogonal ones has chromatic number larger than d. This provides a simple unified characterization of all SIC proofs, including KS, Peres-Mermin, Yu-Oh, and others’ proofs. We apply this result to prove Yu and Oh’s conjecture about the simplest SIC proof and to prove that any SIC set assisted with maximum entanglement generates nonlocality which cannot be improved by nonsignaling resources.
Organiza:
Departamento de Física Atómica, Molecular y Nuclear.
Programa de Doctorado de Excelencia FISYMAT.
Instituto Carlos I de Física Teórica y Computacional.
Hora: 11:00
Lugar: Sala de seminarios de l Seminario de Física Atómica. Tercera Planta de Físicas. Facultad de Ciencias.
Conferenciante: Prof. Adan Cabello. Universidad de Sevilla.
Resumen:
For years, the statement that quantum mechanics exhibits state-independent contextuality (SIC) has been based on a mathematical result pointed out by Kochen and Specker (KS) and Bell: the existence of the so-called KS sets. Recently, Yu and Oh (arXiv:1109.4396) have observed that KS sets are not necessary to prove SIC. Here we show that a set of observables in dimension d represented by rank-1 projectors reveals SIC if and only if the graph in which vertices represent vectors and edges link orthogonal ones has chromatic number larger than d. This provides a simple unified characterization of all SIC proofs, including KS, Peres-Mermin, Yu-Oh, and others’ proofs. We apply this result to prove Yu and Oh’s conjecture about the simplest SIC proof and to prove that any SIC set assisted with maximum entanglement generates nonlocality which cannot be improved by nonsignaling resources.
Organiza:
Departamento de Física Atómica, Molecular y Nuclear.
Programa de Doctorado de Excelencia FISYMAT.
Instituto Carlos I de Física Teórica y Computacional.