Physical EJM Noise Bounds
Abstract
Uniform marginals and L1 control for the physical independently noisy EJM triangle.
Theorem 1.1 (Three independent source deficits bound the full observed law).
Lean statement: D5/S3/Quantum/Entanglement/ElegantJointMeasurementNoiseBounds.ejm_noise_l1_bound
Proof. Machine-checked in Lean as D5/S3/Quantum/Entanglement/ElegantJointMeasurementNoiseBounds.ejm_noise_l1_bound (✓ std3). ∎
Source. Repository-derived.
Commentary.
The visibilities x, y and z belong to [0,1] and refer to the AB, BC and CA singlet sources in the actual six-qubit EJM Born law. The L1 distance sums the absolute probability differences over all 64 ordered outcomes.
The exact eight-term independent-source mixture contains the ideal three-singlet endpoint with weight xyz. All its other terms are nonnegative. Thus the noisy law dominates xyz times the ideal law, and normalization bounds the L1 distance by 2(1-xyz), hence by twice the sum of the three visibility deficits.
The A and B one-party marginals remain exactly 1/4 for every real triple of visibilities as polynomial identities. These are the singletons used by the original inflation score. The L1 result is a physical noise bound, and by itself asserts neither positivity of an inflation certificate nor nonlocality.