Geometrical self-testing of partially entangled two-qubit states

Autor: Satoshi Ishizaka
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: New Journal of Physics, Vol 22, Iss 2, p 023022 (2020)
Druh dokumentu: article
ISSN: 1367-2630
DOI: 10.1088/1367-2630/ab6e49
Popis: Quantum nonlocality has recently been intensively studied in connection to device-independent quantum information processing, where the extremal points of the set of quantum correlations play a crucial role through self-testing. In most protocols, the proofs for self-testing rely on the maximal violation of the Bell inequalities, but there is another known proof based on the geometry of state vectors to self-test a maximally entangled state. We present a geometrical proof in the case of partially entangled states. We show that, when a set of correlators in the simplest Bell scenario satisfies a condition, the geometry of the state vectors is uniquely determined. The realization becomes self-testable when another unitary observable exists on the geometry. Applying this proven fact, we propose self-testing protocols by intentionally adding one more measurement. This geometrical scheme for self-testing is superior in that, by using this as a building block and repeatedly adding measurements, a realization with an arbitrary number of measurements can be self-tested. Besides the application, we also attempt to describe nonlocal correlations by guessing probabilities of distant measurement outcomes. In this description, the quantum set is also convex, and a large class of extremal points is identified by the uniqueness of the geometry.
Databáze: Directory of Open Access Journals