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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.25516 |
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| _version_ | 1866918521127043072 |
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| author | Wang, Fumin |
| author_facet | Wang, Fumin |
| contents | Correlations distributed by a mediator are usually valued for the coordination they enable between authorized agents, but in adversarial settings a more decisive property is whether the same coordination can be inherited by an outside colluder without disturbing the authorized marginal. Classical shared randomness is freely copyable, so a hidden seed coordinating two agents can be duplicated for a third; entanglement is constrained by monogamy, which can forbid such lossless extensions in strongly nonlocal regimes. We turn this asymmetry into an operational resource for private-information games. For a fixed authorized behavior $P_{12}$, we define its \emph{collusive shadow} as the set of relabelled behaviors a colluder can reproduce in any admissible tripartite extension preserving $P_{12}$, and we identify \emph{strategic non-shareability} with the distance from this shadow. We prove that, on finite alphabets, the game-optimized anti-collusion capacity equals the total-variation distance to the shadow; a fixed game provides a task-specific separating witness, while optimization over relabelled games recovers the full distance. In the CHSH score slice, Toner--Verstraete monogamy yields the exact certified frontier, so the Bell local bound $S_{12}=2$ is the sharp onset of positive certified anti-collusion power, saturating at $1/(2\sqrt{2})$ for the maximally entangled CHSH strategy. Classical hidden-variable mediators have zero capacity in this slice. We complement these results with two operational tools: a Hoeffding-based finite-data certification protocol that turns observed Bell scores into confidence-bounded anti-collusion certificates, and a level-2 NPA semidefinite relaxation that extends certified upper envelopes to tilted Bell inequalities. These results recast entanglement monogamy as a measurable shareability deficit for quantum-mediated strategic networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25516 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strategic Non-Shareability of Quantum Correlations Wang, Fumin Quantum Physics Correlations distributed by a mediator are usually valued for the coordination they enable between authorized agents, but in adversarial settings a more decisive property is whether the same coordination can be inherited by an outside colluder without disturbing the authorized marginal. Classical shared randomness is freely copyable, so a hidden seed coordinating two agents can be duplicated for a third; entanglement is constrained by monogamy, which can forbid such lossless extensions in strongly nonlocal regimes. We turn this asymmetry into an operational resource for private-information games. For a fixed authorized behavior $P_{12}$, we define its \emph{collusive shadow} as the set of relabelled behaviors a colluder can reproduce in any admissible tripartite extension preserving $P_{12}$, and we identify \emph{strategic non-shareability} with the distance from this shadow. We prove that, on finite alphabets, the game-optimized anti-collusion capacity equals the total-variation distance to the shadow; a fixed game provides a task-specific separating witness, while optimization over relabelled games recovers the full distance. In the CHSH score slice, Toner--Verstraete monogamy yields the exact certified frontier, so the Bell local bound $S_{12}=2$ is the sharp onset of positive certified anti-collusion power, saturating at $1/(2\sqrt{2})$ for the maximally entangled CHSH strategy. Classical hidden-variable mediators have zero capacity in this slice. We complement these results with two operational tools: a Hoeffding-based finite-data certification protocol that turns observed Bell scores into confidence-bounded anti-collusion certificates, and a level-2 NPA semidefinite relaxation that extends certified upper envelopes to tilted Bell inequalities. These results recast entanglement monogamy as a measurable shareability deficit for quantum-mediated strategic networks. |
| title | Strategic Non-Shareability of Quantum Correlations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.25516 |