Lifting noncontextuality inequalities (Phys. Rev. A 109, 052216, arXiv:2401.12349)
Authors: RC, Rui Soares Barbosa, Adán Cabello
It was shown by Stefano Pironio that given any facet-inducing inequality of a Bell scenario S and an extension of S to another Bell scenario T, testing the same inequality (effectively) preserves its stature as a facet-inducing inequality for T, a phenomenon known as lifting. In our work, we extended Pironio's results from Bell to KS non-contextuality scenarios. The idea being that if you start with a facet-inducing inequality of any Kochen-Specker (KS) non-contextuality scenario, then any arbitrary extension of the initial scenario preserves the inequality's stature as facet-inducing for the extended scenario. We further provide examples of facet-inducing KS inequalities of scenarios for which no NC inequalities were hitherto known. This is because for any scenario to witness contextuality its compatibility structure must have an induced n-cycle (n ≥ 4) inside it as is dictated by Vorob'ev’s theorem. Since all the facet-inducing inequalities of the n-cycle KS scenarios are known, our result offers itself to provide a subset of facet-inducing inequalities for any arbitrary contextuality witnessing scenario .
E-principle and Ramsey numbers (doi.org/10.48550/arXiv.2411.09773 )
Authors: RC, Som Kanjilal, Rui Soares Barbosa
Contextual (non-local) vertices of a no-disturbance (no-signalling) polytope aren't quantum realizable as was shown in [Phys. Rev. Lett. 117, 050401]. Therefore, any principle (or set of principles) aiming to single out quantum theory out of all the no-disturbance theories has a bare minimum benchmark test to pass: it must detect these contextual vertices as non-quantum i.e. post-quantum. To this end, among the already known principles, E-principle popularly known as the Local orthogonality principle, is the only that has detected non-local vertices of the yet explored Bell polytopes as post-quantum.
A usual way to test this is to construct exclusivity graph of a given non-local extremal box and then take independent copies of it to construct a joint exclusivity graph (via the OR graph product) to look for a clique inside it for which the E-principle is violated. This is known as the activation effect of E-principle and is traditionally explored via brute-force methods. Here we study these activation effects within n-cycle KS non-contextuality scenarios and provide an intriguing connection of finding violation producing cliques with the (in) famous problem of finding Ramsey numbers.
Using known results in Ramsey theory literature we exhibit: why in [Nature Communications 4, 2263 (2013)], using two copies of the PR box, the authors could only (brute-forcely) find minimal violation of E-principle and nothing beyond; why for a given size k ≥ 4 of the allowed independent copies of the contextual extremal box, there is a range of n-cycle scenarios whose contextual extremal boxes won't violate E-principle; for k = 2 & 3 copies we show that only n = 4,5 (i.e. CHSH and KCBS) contextual extremal boxes can produce violation of E-principle i.e. no contextual box for n ≥ 6 cycle scenario witnesses violation with two or three copies. Furthermore, we provide the exact construction of violation producing cliques for any k ≥ 2, when n = 4,5.
Contextuality with Pauli observables in cycle scenarios (doi.org/10.48550/arXiv.2411.09773 )
Authors: RC, Rui Soares Barbosa
In [Phys. Rev. Lett. 123, 200501] Kirby and Love provided necessary and sufficient conditions to test whether a given set of qubit Pauli operators can be enlarged (by taking products of these Pauli operators) to produce a state independent proof of contextuality i.e. a Peres-Mermin magic square like proof. But what if we don't allow the extension of the original set of Pauli operators and instead look for contextuality just within this set? We would have to give up on the search of state-independent proofs of contextuality and instead try to characterise as to when qubit Pauli operators can violate a non-contextuality inequality.
Given many nice properties of Pauli operators maybe there is an interesting answer to this question. In this work we analysed this and focused on the violation of n-cycle KS non-contextuality inequalities when the quantum measurements were restricted to qubit Pauli operators. In doing so we provide an upper bound on the size of cycles realizable (faithfully) by qubit Pauli operators as their compatibility structure. More specifically, we showed that for a given number, say k, of qubits, the k-qubit Pauli operator can only realize a cycle of size atmost 3k.
We then show that among all possible cycles realizable (faithfully) by Pauli operators, only the 4-cycle can witness contextuality and that too maximally and irrespective of k, the number of qubits. We then explore arbitrary scenarios where we show that the presence of a 4-cycle inside any scenario's compatibility graph is sufficient but not necessary for qubit Pauli operators to witness contextuality. We exhibit this by providing Pauli realizable compatibility graphs that have no induced 4-cycle but still witness contextuality.
Bipartite extremal non-signalling non-PR boxes, minimal decomposition of the magic square correlations, and local orthogonality (to be out soon)
Authors: Emmanuel Zambrini/Junior R. Gonzales-Ureta, RC, Adán Cabello
Need to ask for co-authors' permission before I give out some details here