Violation of steering inequality for generalized equiangular measurements

Abstract

In this article, we study bipartite quantum steering using a general class of measurement operators known as the generalized equiangular measurement (GEAM). Our approach allows for the construction of steering inequalities that are applicable not only to informationally complete measurements but also to incomplete or lossy scenarios, where the resulting quantum assemblages may be subnormalized. We develop a method to analytically bound the value of steering functionals under local hidden state (LHS) models by employing a generalized inequality for the eigenvalues of positive semidefinite operators, extending classical results such as the Samuelson inequality. This yields universal upper bounds on the LHS value in terms of the parameters defining the frame. Furthermore, we analyze the asymptotic behavior of these bounds in high-dimensional Hilbert spaces and demonstrate the possibility of unbounded quantum violations of steering inequalities. Our formalism encompasses previously known results for mutually unbiased bases (MUBs) and mutually unbiased measurements (MUMs) as special cases, showing that these are particular instances within a unified and more general framework.

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