ω_co is approached by projective strategies in dyadic pairs #
Work package T5 of C6b (planning/c6b-plan.md; reports/c6b-paper-proofs.md, §3): below
ω_co(G), and above 0, lies the value of a projective strategy for G in a dyadic pair
(MIPRE.CommutingFinitePairApprox, lem:co-value-finite-pair). The proof is that of the finite
pair form, run on an amplified strategy:
- Strict tracial reduction into dyadic pairs (
exists_tracialStrategy_isDyadicPair): belowω_co(G)lies the winning probability of a tracial strategy whose standard-form model is a dyadic pair in every state. It is Lin's strict tracial reduction followed by amplification by the twisted Pauli algebra (Pauli.pauliStd, which has unital dyadic matrix units,Pauli.pauliStd_hasDyadicUnits), at no cost in correlation (Theorems A and T). - Projectivity (
exists_projStrat_expand_stdModel): the strategy is a projective strategy, of value its winning probability, of an ancilla extension of its standard-form model with nonempty registers, which is again a dyadic pair (BipartiteModel.IsDyadicPair.expand).
ω_co is approached by projective strategies in dyadic pairs (lem:co-value-finite-pair):
below ω_co(G), and above 0, lies the value of a projective strategy for G in a dyadic pair on
a Hilbert space of Type, the ancilla extension of the standard-form model of a tracial strategy
amplified by the twisted Pauli algebra.