Device-Independent Self-Testing of the Three-Qubit CCZ Hypergraph State

• URL: http://arxiv.org/abs/2607.21288v1
• Date: Thu, 23 Jul 2026 13:09:18 GMT
• Title: Device-Independent Self-Testing of the Three-Qubit CCZ Hypergraph State
• Abstract summary: We show that twenty correlators, all obtainable from five of the eight global input triples in the tripartite two-input, two-output scenario, determine the CCZ state.<n>We construct an explicit Bell inequality whose maximal quantum violation self-tests the CCZ state and all three local measurements.
• Score: 7.460125778763875
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The three-qubit CCZ state is the smallest rank-three hypergraph state and an elementary entangled magic resource. Its cubic phase is governed by generalized stabilizers that are not Pauli strings, so standard graph-state self-testing arguments do not apply directly. We show that twenty correlators, all obtainable from five of the eight global input triples in the tripartite two-input, two-output scenario, determine this state and the action of the Pauli $X/Z$ measurements up to local isometries. The proof fixes eight equally weighted computational branches and propagates conditional $X$-flip relations across the branch cube, recovering the minus sign of the $111$ amplitude. These five-context correlations are nonlocal, but the canonical Pauli measurements cannot attain the largest quantum value of any Bell inequality that they violate: whenever they maximize a Bell expression, its local bound has the same value. Introducing an independent third measurement makes self-testing from maximal Bell violation possible. We construct an explicit Bell inequality whose maximal quantum violation self-tests the CCZ state and all three local measurements. An exact sum-of-squares decomposition proves the quantum bound, and its equality conditions yield an analytic SWAP extraction. Together, these results give two explicit device-independent self-tests of the CCZ state and demonstrate that determining a state and its measurements from several correlator equalities is distinct from identifying them through the maximal violation of a single Bell inequality.

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