Characterizing finite-dimensional quantum behavior

Autor(en)

Miguel Navascués, Adrien Feix, Mateus Araújo, Tamás Vertési

Abstrakt

We study and extend the semidefinite programming (SDP) hierarchies introduced in Navascués and Vértesi [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of the statistical correlations arising from finite-dimensional quantum systems. First, we introduce the dimension-constrained noncommutative polynomial optimization (NPO) paradigm, where a number of polynomial inequalities are defined and optimization is conducted over all feasible operator representations of bounded dimensionality. Important problems in device-independent and semi-device-independent quantum information science can be formulated (or almost formulated) in this framework. We present effective SDP hierarchies to attack the general dimension-constrained NPO problem (and related ones) and prove their asymptotic convergence. To illustrate the power of these relaxations, we use them to derive a number of dimension witnesses for temporal and Bell-type correlation scenarios, and also to bound the probability of success of quantum random access codes.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Österreichische Akademie der Wissenschaften (ÖAW), Magyar Tudományos Akadémia

Journal

Physical Review A

Band

92

Anzahl der Seiten

15

ISSN

1050-2947

Publikationsdatum

10-2015

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik

Schlagwörter

ASJC Scopus Sachgebiete

Atomic and Molecular Physics, and Optics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/5c79081e-377b-43a9-97a0-c95fc6b5c43e