Details
| Original language | English |
|---|---|
| Article number | 073003 |
| Journal | New journal of physics |
| Volume | 25 |
| Issue number | 7 |
| Publication status | Published - 10 Jul 2023 |
| Externally published | Yes |
Abstract
Quantum contextuality is one of the most recognized resources in quantum communication and computing scenarios. We provide a new quantifier of this resource, the rank of contextuality (RC). We define RC as the minimum number of non-contextual behaviors that are needed to simulate a contextual behavior. We show that the logarithm of RC is a natural contextuality measure satisfying several properties considered in the spirit of the resource-theoretic approach. The properties include faithfulness, monotonicity, and additivity under tensor product. We also give examples of how to construct contextual behaviors with an arbitrary value of RC exhibiting a natural connection between this quantifier and the arboricity of an underlying hypergraph. We also discuss exemplary areas of research in which the new measure appears as a natural quantifier.
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: New journal of physics, Vol. 25, No. 7, 073003, 10.07.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The rank of contextuality
AU - Horodecki, Karol
AU - Zhou, Jingfang
AU - Stankiewicz, Maciej
AU - Salazar, Roberto
AU - Horodecki, Paweł
AU - Raussendorf, Robert
AU - Horodecki, Ryszard
AU - Ramanathan, Ravishankar
AU - Tyhurst, Emily
N1 - Funding Information: KH acknowledges National Science Centre, Poland, Grant Sonata Bis 5, 2015/18/E/ST2/00327 and National Science Centre, Poland, Grant OPUS 9, 2015/17/B/ST2/01945. MS acknowledges National Science Centre, Poland, Grant SHENG 1, 2018/30/Q/ST2/00625. RS acknowledges financial support by the Foundation for Polish Science through TEAM-NET project (Contract No. POIR.04.04.00-00-17C1/18-00). We acknowledge partial support by the Foundation for Polish Science (IRAP project, ICTQT, Contract No. MAB/2018/5, co-financed by EU within Smart Growth Operational Programme). The ‘International Centre for Theory of Quantum Technologies’ project (Contract No. MAB/2018/5) is carried out within the International Research Agendas Programme of the Foundation for Polish Science co-financed by the European Union from the funds of the Smart Growth Operational Programme, axis IV: Increasing the research potential (Measure 4.3).
PY - 2023/7/10
Y1 - 2023/7/10
N2 - Quantum contextuality is one of the most recognized resources in quantum communication and computing scenarios. We provide a new quantifier of this resource, the rank of contextuality (RC). We define RC as the minimum number of non-contextual behaviors that are needed to simulate a contextual behavior. We show that the logarithm of RC is a natural contextuality measure satisfying several properties considered in the spirit of the resource-theoretic approach. The properties include faithfulness, monotonicity, and additivity under tensor product. We also give examples of how to construct contextual behaviors with an arbitrary value of RC exhibiting a natural connection between this quantifier and the arboricity of an underlying hypergraph. We also discuss exemplary areas of research in which the new measure appears as a natural quantifier.
AB - Quantum contextuality is one of the most recognized resources in quantum communication and computing scenarios. We provide a new quantifier of this resource, the rank of contextuality (RC). We define RC as the minimum number of non-contextual behaviors that are needed to simulate a contextual behavior. We show that the logarithm of RC is a natural contextuality measure satisfying several properties considered in the spirit of the resource-theoretic approach. The properties include faithfulness, monotonicity, and additivity under tensor product. We also give examples of how to construct contextual behaviors with an arbitrary value of RC exhibiting a natural connection between this quantifier and the arboricity of an underlying hypergraph. We also discuss exemplary areas of research in which the new measure appears as a natural quantifier.
KW - contextuality
KW - nonlocality
KW - quantum
UR - http://www.scopus.com/inward/record.url?scp=85164916994&partnerID=8YFLogxK
U2 - 10.1088/1367-2630/acdf78
DO - 10.1088/1367-2630/acdf78
M3 - Article
AN - SCOPUS:85164916994
VL - 25
JO - New journal of physics
JF - New journal of physics
SN - 1367-2630
IS - 7
M1 - 073003
ER -