2025/08/23 by Ibnouhsein, Issam
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2508.17075
The process-matrix framework models quantum correlations without assuming a predefined global causal order, yet its standard Choi-Jamiolkowski construction implicitly presupposes a globally aligned Hilbert-space basis across all local laboratories. This makes the formalism causally indefinite yet kinematically absolute. To achieve full relational consistency, we impose the principle of local frame independence: physical predictions must remain invariant under independent unitary redefinitions of each laboratory's local basis. We formalize this requirement as a local gauge symmetry and derive the corresponding covariant representation of any process by averaging over the symmetry group. The image of this twirling operation forms a strict subset of the cone of causally separable processes. Covariance thus enforces a superselection rule for causal order, showing that indefinite causal order is not an intrinsic feature of nature but a relational coherence that exists only relative to a physical system establishing a shared quantum reference frame.