The two-qubit Hardy ladder: the closed form P_K*(q) and its unique maximiser for every K, Hardy's optimum at K = 1, and the optimum (8 rho^2 + rho - 11)/25 in the cubic field Q(rho) at K = 2
Kernel-checked optimum of Hardy's K-step ladder for two qubits (Hardy 1993; Hardy 1997; Boschi, Branca, De Martini and Hardy 1997), for a real Schmidt state c0|00> + c1|11> and real projective settings, the probabilities written out as squared real amplitudes. For every K: under the ladder constraints P(A_K = 1, B_K = 1) 0 and every large enough K some state and settings exceed 1/2 - eps (the "(50 - delta)%" of Hardy 1997 and Boschi et al. 1997). For every K >= 1 the maximiser of the closed form on (0, 1) is the unique zero there of Cereceda's polynomial m_K (Cereceda 2002, eq. (20), stated…
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