Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/24578
Title: 
Authors: 
Keywords: 
Nonlocality
Quantum correlations in quantum information
Quantum entanglement
Issue Date: 
2022
Citation: 
Kishor Bharti, Ray, M., Xu, Z.-P., Hayashi, M., Kwek, L.-C., & Cabello, A. (2022). Graph-theoretic approach for self-testing in Bell scenarios. PRX Quantum, 3(3), Article 030344. https://doi.org/10.1103/prxquantum.3.030344
Journal: 
PRX Quantum
Abstract: 
Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set BQ of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, BQ is difficult to characterize, so it is also difficult to prove whether or not a given matrix of quantum correlations allows for self-testing. Here, we show how some tools from graph theory can help to address this problem. We observe that BQ is strictly contained in an easy-to-characterize set associated with a graph, Θ(G). Therefore, whenever the optimum over BQ and the optimum over Θ(G)) coincide, self-testing can be demonstrated by simply proving self-testability with Θ(G). Interestingly, these maxima coincide for the quantum correlations that maximally violate many families of Bell-like inequalities. Therefore, we can apply this approach to prove the self-testability of many quantum correlations, including some that are not previously known to allow for self-testing. In addition, this approach connects self-testing to some open problems in discrete mathematics. We use this connection to prove a conjecture [M. Araujo et a/., Phys. Rev. A, 88, 022118 (2013)] about the closed-form expression of the Lovasz theta number for a family of graphs called the Mobius ladders. Although there are a few remaining issues (e.g., in some cases, the proof requires the assumption that measurements are of rank 1). this approach provides an alternative method to self-testing and draws interesting connections between quantum mechanics and discrete mathematics.
Description: 
The open access publication is available at: https://doi.org/10.1103/prxquantum.3.030344
URI: 
ISSN: 
2691-3399
DOI: 
File Permission: 
None
File Availability: 
No file
Appears in Collections:Journal Articles

Show full item record

Page view(s)

15
checked on Jan 26, 2023

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.