Hidden-Field Coordination Reveals Payoff-Free Quantum Correlation Structure in Decentralized Coordination

Abstract

We study decentralized multi-agent coordination where agents must correlate actions against an unobserved field and cannot communicate. To isolate correlation geometry from payoff optimization, we introduce the Hidden-Field Coordination (HFC) model, which enforces identical information access and no-signaling constraints across strategies. Using information-theoretic diagnostics, we compare classical shared-randomness baselines with an entanglement-mediated strategy based on multipartite W states and a strictly local Spontaneous Leader Election rule. Within the restricted symmetric shared-latent baseline studied here, increasing total correlation is achieved primarily by driving actions toward alignment (copying), which also increases pairwise coincidence (collisions). By contrast, the quantum strategy realizes a collision-suppressing coordination regime: it preserves global dependence while reducing pairwise coincidence below the independent (product) baseline induced by the common marginal distribution. This produces a geometric separation in the joint-action distribution. Classical baselines concentrate probability near the diagonal of action equality, whereas the entanglement-mediated mapping occupies an offset-diagonal region associated with relational roles. Accordingly, the entanglement signature in this setting is not higher correlation magnitude; total-correlation differentials can be negative relative to the classical copying optimum. Instead, it reflects a change in dependence geometry that supports robust anti-coordination.

Figures (8)

• Figure 1: Schematic of the Hidden-Field Coordination (HFC) model and strategy families. Each round samples a latent hidden field $F$ that remains unobserved by agents and influences only the local intel perturbations (rate $p$). Agents act without communication; correlation arises solely from a pre-shared resource established prior to the round. We compare independent sampling, classical shared-latent coordination (shared variable $L$), and quantum-correlated coordination (shared state (e.g. $|W_N\rangle$)). The analyzed object is the empirical joint-action distribution $P(a_1,\ldots,a_N)$, from which payoff-free diagnostics (APMI, total correlation TC, and differentials $\Delta \mathcal{M}$ relative to the best classical baseline) are computed.
• Figure 2: Representative joint-action maps for team sizes $N=3$ (top) and $N=5$ (bottom). The shared-latent model (middle panels, diagonal strips, $q=0.7$) shows concentration along the $a_1 = a_2$ diagonal, indicating coordination achieved through action alignment (copying). In contrast, the quantum strategy (right panels) displays an "L-shaped" relational structure. Probabilities are concentrated where one agent is the Leader ($a=1$) and others are Followers ($a \neq 1$), effectively distributing probability mass away from the collision point at $(1,1)$.
• Figure 3: Coordination geometry trails for $N=3$ (top) and $N=5$ (bottom). The shared-latent classical model (black squares) traces a path toward high coincidence, confirming that the restricted shared-latent classical baseline increases correlation (APMI) primarily through alignment. The quantum strategy (blue triangles) occupies a distinct region characterized by stable APMI but low coincidence, sitting below the independent baseline (grey dashed line). This reveals a geometric separation relative to the restricted shared-latent classical baseline: entanglement circumvents the trade-off between coordination and collision risk within that baseline family.
• Figure 4: Differential Total Correlation $\Delta \mathrm{TC}$ for $N=3$ and $N=5$. Consistently negative values across the noise ($\lambda$) and intel ($p$) sweep confirm that the classical baseline achieves higher raw dependence via alignment. The quantum strategy utilizes the $W$ state to generate relational correlations, sacrificing total shared information to remain in a low-collision regime.
• Figure 5: Pairwise-structure differential $\Delta \mathrm{APMI}$ between the quantum strategy and the best classical baseline across intel rate $p$ and depolarizing strength $\lambda$, shown for $N=3$ (left) and $N=5$ (right). Here $\Delta \mathrm{APMI} = \mathrm{APMI}_{\mathrm{quant}} - \max\!\left(\mathrm{APMI}_{\mathrm{ind}}, \max_{q\in[0,1]}\mathrm{APMI}_{\mathrm{shared}}(q)\right)$ evaluated locally at each$(p,\lambda)$. The consistently negative or near-zero differentials highlight that the quantum strategy does not aim to maximize raw information-theoretic magnitude. Instead, its primary advantage lies in the geometric distribution of those correlations (lower coincidence) relative to the classical baseline, which is forced into action-alignment to achieve comparable APMI levels.