The Arity–Resonance Ceiling: Why Pauli Contextuality Stops at $H^3$

The repair price of a contextuality scenario is the minimum number of elementary outcome merges whose simultaneous application restores a global section. On binary scenarios it is an affine reparametrisation of the optimum of Min-Rep / LABEL-COVER_min: pi(e) = MinRep(e) - |Q| for Q the site set. The minimisation is therefore twenty-five years old and is not claimed as new; the contribution is the transfer and what it buys in both directions - an additive hardness of approximation for the repair price, and for the hardness-of-approximation quantity a reading as a physical repair cost that vanishes exactly on the non-contextual scenarios. The identity does not survive past binary arity: at arity three the two quantities can separate (pi = 3 against MinRep_gen - |Q| = 1 on an explicit witness), while equality persists on others including Mermin and GHZ, so strictness is exhibited and not generic. Also given: a monotone integer ledger along scenario growth, an incidence law at the price floor stated as a bounded exhaustion with its converse killed by a shipped witness, a measured separation from contextuality degree (flat where the repair price grades, and undefined on scenarios where the repair price is still defined), a complement to Arkhipov's arrangement theorem in the regime his theorem leaves open (stated as a conjecture), and an exact statement of the domain on which the repair price is identically zero. Two stdlib-only verification engines reproduce every recomputable number on three cross-asserted routes, and the complete pre-release review record - two blind refutation-first referee rounds, the repair log, and the residual confirmation - ships with the paper.The repair price of a contextuality scenario is the minimum number of elementary outcome merges whose simultaneous application restores a global section. On binary scenarios it is an affine reparametrisation of the optimum of Min-Rep / LABEL-COVER_min: pi(e) = MinRep(e) - |Q| for Q the site set. The minimisation is therefore twenty-five years old and is not claimed as new; the contribution is the transfer and what it buys in both directions - an additive hardness of approximation for the repair price, and for the hardness-of-approximation quantity a reading as a physical repair cost that vanishes exactly on the non-contextual scenarios. The identity does not survive past binary arity: at arity three the two quantities can separate (pi = 3 against MinRep_gen - |Q| = 1 on an explicit witness), while equality persists on others including Mermin and GHZ, so strictness is exhibited and not generic. Also given: a monotone integer ledger along scenario growth, an incidence law at the price floor stated as a bounded exhaustion with its converse killed by a shipped witness, a measured separation from contextuality degree (flat where the repair price grades, and undefined on scenarios where the repair price is still defined), a complement to Arkhipov's arrangement theorem in the regime his theorem leaves open (stated as a conjecture), and an exact statement of the domain on which the repair price is identically zero. Two stdlib-only verification engines reproduce every recomputable number on three cross-asserted routes, and the complete pre-release review record - two blind refutation-first referee rounds, the repair log, and the residual confirmation - ships with the paper.

Aug 10, 20260 citations

On the Possibility of Pauli Principle Violation in Atoms

Lev B. Okun

Jan 1, 198779 citations

Contextuality with Pauli observables in cycle scenarios

Choudhary, Raman, Rui Soares Barbosa

Contextuality is a fundamental marker of quantum non-classicality, which has emerged as a key resource for quantum computational advantage in multiple settings. Many such results hinge specifically on contextuality witnessed through Pauli measurements. In this work, we initiate a systematic study of (state-dependent) Pauli contextuality, focusing on cycle measurement scenarios, the simplest scenarios capable of exhibiting contextual behaviour. First, we study realizability of cycle scenarios with multi-qubit Pauli observables: we show that the maximum size of a cycle faithfully realizable by $m$ -qubit Paulis is upper bounded by $3m$ , while we construct explicit realizations of cycles of size $2m-1$ or $2m$ , depending on whether $m \not\equiv 1 \pmod{3}$ or $m \equiv 1 \pmod{3}$ . Then, we investigate the presence of contextuality: we prove that no $n$ -cycle Pauli realization for $n > 4$ can witness contextuality (on any quantum state), whereas for $n = 4$ every Pauli realization exhibits contextuality, attaining the quantum bound for all noncontextuality inequalities on some pure state. Finally, we discuss arbitrary Pauli scenarios in light of Vorob'ev's theorem, and show that, contrary to what our cycle characterization might suggest, the presence of $4$ -cycles is not necessary for witnessing contextuality in general Pauli scenarios.Contextuality is a fundamental marker of quantum non-classicality, which has emerged as a key resource for quantum computational advantage in multiple settings. Many such results hinge specifically on contextuality witnessed through Pauli measurements. In this work, we initiate a systematic study of (state-dependent) Pauli contextuality, focusing on cycle measurement scenarios, the simplest scenarios capable of exhibiting contextual behaviour. First, we study realizability of cycle scenarios with multi-qubit Pauli observables: we show that the maximum size of a cycle faithfully realizable by $m$-qubit Paulis is upper bounded by $3m$, while we construct explicit realizations of cycles of size $2m-1$ or $2m$, depending on whether $m \not\equiv 1 \pmod{3}$ or $m \equiv 1 \pmod{3}$. Then, we investigate the presence of contextuality: we prove that no $n$-cycle Pauli realization for $n > 4$ can witness contextuality (on any quantum state), whereas for $n = 4$ every Pauli realization exhibits contextuality, attaining the quantum bound for all noncontextuality inequalities on some pure state. Finally, we discuss arbitrary Pauli scenarios in light of Vorob'ev's theorem, and show that, contrary to what our cycle characterization might suggest, the presence of $4$-cycles is not necessary for witnessing contextuality in general Pauli scenarios.

arXiv:2502.03451Feb 5, 20250 citations

An axiomatic deduction of the pauli spinor theory

H. M. Schwartz

International Journal of Theoretical PhysicsApr 1, 19772 citations

The Arity–Resonance Ceiling: Why Pauli Contextuality Stops at

H^3

m

-qubit Paulis is upper bounded by

3m

, while we construct explicit realizations of cycles of size

2m-1

2m

, depending on whether

m \not\equiv 1 \pmod{3}

m \equiv 1 \pmod{3}

. Then, we investigate the presence of contextuality: we prove that no

n

-cycle Pauli realization for

n > 4

can witness contextuality (on any quantum state), whereas for

n = 4

every Pauli realization exhibits contextuality, attaining the quantum bound for all noncontextuality inequalities on some pure state. Finally, we discuss arbitrary Pauli scenarios in light of Vorob'ev's theorem, and show that, contrary to what our cycle characterization might suggest, the presence of

4

-cycles is not necessary for witnessing contextuality in general Pauli scenarios.