Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1112.5149

State-independent quantum contextuality and maximum nonlocality

Adán Cabello

Published Dec 21, 2011• 10 citations
arXivHTMLPDF

Abstract

Recently, Yu and Oh [Phys. Rev. Lett. 108, 030402 (2012)] have conjectured that the simplest set of vectors needed to prove state-independent contextuality on a qutrit requires 13 vectors. Here we first prove that a necessary and sufficient condition for a set of vectors in any dimension $d \ge 3$ to prove contextuality for a system prepared in a maximally mixed state is that the graph $G_C$ in which vertices represent vectors and edges link orthogonal ones has chromatic number $χ(G_G)$ larger than $d$. Then, we prove Yu and Oh's conjecture. Finally, we prove that any set satisfying $χ(G_G)>d$ assisted with $d$-party maximum entanglement generates nonlocality which cannot be improved without violating the no-signalling principle. This shows that any set satisfying $χ(G_G)>d$ is a valuable resource for quantum information processing.

DOI
10.48550/arxiv.1112.5149

Related papers

Minimal proofs of state-independent contextuality

Adán Cabello

It has been recently shown that state-independent contextuality (SIC) is a fundamental resource linked with a type of nonlocality which cannot be improved by nonsignaling resources. Therefore, it is of fundamental importance to identify the simplest sets of quantum observables needed to prove SIC. We show that d+10 rank-1 projectors are sufficient to prove SIC for any physical system in dimension d>2. This result outperforms both the best Kochen-Specker proofs and the results presented by Yu and Oh in arXiv:1112.5513v1.

arXiv:1201.0374•Jan 1, 2012•3 citations

Necessary and Sufficient Condition for State-Independent Contextual Measurement Scenarios

Ravishankar Ramanathan, Paweł Horodecki

The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension d and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes of contextual behavior, and that (ii) state-independent contextuality is equivalent to the contextuality of the maximally mixed state up to a global unitary transformation. We then derive a necessary and sufficient condition for a measurement scenario represented by an orthogonality graph to reveal state-independent contextuality. This condition is given in terms of the fractional chromatic number of the graph χf(G) and is shown to identify all state-independent contextual measurement scenarios including those that go beyond the original Kochen-Specker paradigm.

arXiv:1212.5933•Physical Review Letters•Jan 29, 2014•36 citations

Experimental test of state-independent quantum contextuality of an indivisible quantum system

Yun‐Feng Huang, Meng Li, Dong-Yang Cao +5 more

We report a state-independent experimental test of quantum contextuality of a single-photon qutrit. The experimental results demonstrate violations of an inequality originally formulated by Yu and Oh [Phys. Rev. Lett. 108, 030402 (2012)] and further optimized by Cabello et al. [Phys. Rev. A 85, 032108 (2012)]; this inequality is satisfied by all noncontextual hidden variable models and is violated by all qutrit states. Our experiment shows quantum contextuality of this nature in a most fundamental way: A way that is independent of state and unrelated to entanglement.

Physical Review A•May 24, 2013•25 citations

Hardy's Paradox for Yu-Oh Set Constructed by Logically Contextual Quantum States

Chang He, Yongjun Wang, Baoshan Wang +2 more

Quantum contextuality is a fundamental nonclassical property of quantum systems, regarded as a key resource that demonstrates the computational and informational advantages of quantum over classical systems. Our present work aims to construct Hardy's paradoxes, a set of possibilistic conditions witnessing contextuality, for Yu-Oh set, which is the state-independent contextual quantum system with the least number of vectors. To achieve the aim, we systematically enumerate all logically contextual pure states on Yu-Oh set, and theoretically prove that no mixed states in this scenario are logically contextual. Based on the identified logically contextual quantum states, we construct 12 Hardy's paradoxes with identical success probability SP=11.1%. Furthermore, we present corresponding observables to experimentally witness these Hardy's paradoxes.

quant-pharXiv:2603.12738•Mar 16, 2026•0 citations

Necessary and Sufficient Condition for Quantum State-Independent Contextuality

Adán Cabello, Matthias Kleinmann, Costantino Budroni

We solve the problem of whether a set of quantum tests reveals state-independent contextuality and use this result to identify the simplest set of the minimal dimension. We also show that identifying state-independent contextuality graphs [R. Ramanathan and P. Horodecki, Phys. Rev. Lett. 112, 040404 (2014)] is not sufficient for revealing state-independent contextuality.

arXiv:1501.03432•Physical Review Letters•Jun 24, 2015•51 citations

Quantum state-independent contextuality requires 13 rays

Adán Cabello, Matthias Kleinmann, José R. Portillo

Abstract We show that, regardless of the dimension of the Hilbert space, there exists no set of rays revealing state-independent contextuality with less than 13 rays. This implies that the set proposed by Yu and Oh in dimension three (2012 Phys. Rev. Lett. 108 030402 ) is actually the minimal set in quantum theory. This contrasts with the case of Kochen–Specker sets, where the smallest set occurs in dimension four.

arXiv:1606.01848•Journal of Physics A Mathematical and Theoretical•Aug 30, 2016•50 citations
Recently, Yu and Oh [Phys. Rev. Lett. 108, 030402 (2012)] have conjectured that the simplest set of vectors needed to prove state-independent contextuality on a qutrit requires 13 vectors. Here we first prove that a necessary and sufficient condition for a set of vectors in any dimension d≥3d \ge 3d≥3 to prove contextuality for a system prepared in a maximally mixed state is that the graph GCG_CGC​ in which vertices represent vectors and edges link orthogonal ones has chromatic number χ(GG)χ(G_G)χ(GG​) larger than ddd. Then, we prove Yu and Oh's conjecture. Finally, we prove that any set satisfying χ(GG)>dχ(G_G)>dχ(GG​)>d assisted with ddd-party maximum entanglement generates nonlocality which cannot be improved without violating the no-signalling principle. This shows that any set satisfying χ(GG)>dχ(G_G)>dχ(GG​)>d is a valuable resource for quantum information processing.
It has been recently shown that state-independent contextuality (SIC) is a fundamental resource linked with a type of nonlocality which cannot be improved by nonsignaling resources. Therefore, it is of fundamental importance to identify the simplest sets of quantum observables needed to prove SIC. We show that d+10 rank-1 projectors are sufficient to prove SIC for any physical system in dimension d>2. This result outperforms both the best Kochen-Specker proofs and the results presented by Yu and Oh in arXiv:1112.5513v1.
The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension d and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes of contextual behavior, and that (ii) state-independent contextuality is equivalent to the contextuality of the maximally mixed state up to a global unitary transformation. We then derive a necessary and sufficient condition for a measurement scenario represented by an orthogonality graph to reveal state-independent contextuality. This condition is given in terms of the fractional chromatic number of the graph χf(G) and is shown to identify all state-independent contextual measurement scenarios including those that go beyond the original Kochen-Specker paradigm.
We report a state-independent experimental test of quantum contextuality of a single-photon qutrit. The experimental results demonstrate violations of an inequality originally formulated by Yu and Oh [Phys. Rev. Lett. 108, 030402 (2012)] and further optimized by Cabello et al. [Phys. Rev. A 85, 032108 (2012)]; this inequality is satisfied by all noncontextual hidden variable models and is violated by all qutrit states. Our experiment shows quantum contextuality of this nature in a most fundamental way: A way that is independent of state and unrelated to entanglement.
Quantum contextuality is a fundamental nonclassical property of quantum systems, regarded as a key resource that demonstrates the computational and informational advantages of quantum over classical systems. Our present work aims to construct Hardy's paradoxes, a set of possibilistic conditions witnessing contextuality, for Yu-Oh set, which is the state-independent contextual quantum system with the least number of vectors. To achieve the aim, we systematically enumerate all logically contextual pure states on Yu-Oh set, and theoretically prove that no mixed states in this scenario are logically contextual. Based on the identified logically contextual quantum states, we construct 12 Hardy's paradoxes with identical success probability SP=11.1%. Furthermore, we present corresponding observables to experimentally witness these Hardy's paradoxes.