EPR-steering boundaries from a universal spectral equation

Abstract

We determine EPR-steering boundaries from a universal spectral equation for the common hidden-state ensemble underlying remote conditional preparations. In arbitrary finite-dimensional bipartite systems, its solution gives the ensemble weights, with limiting mass equal to the steering scale. For qubits, algebraic and integral formulas eliminate measurement variables and resolve outcome partitions, making both projective and generalized-measurement scales exactly evaluable at all parameters. Further analytical solution reconstructs the optimal hidden-state distribution on a domain of biased, anisotropic states. Along an explicit family, the white noise tolerated by projective steering halves while the boundary negativity stays at $1/8$. For the original Bowles states, we obtain the complete one-way interval under arbitrary measurements.