Speaker
Description
In quantum theory, POVMs form the maximal class of measurements compatible with the Born rule. Operational reconstructions motivate a broader convex framework—General Probabilistic Theories (GPTs)—specified by a convex state space and its dual cone of affine measurement functionals.
Within GPTs one can define “non-positive POVMs” (N-POVMs): Hermitian effects summing to the unit but not positive semidefinite. Although invalid on the full quantum state space, they are mathematically well-defined on suitable convex domains where all outcome probabilities are nonnegative and can outperform genuine POVMs on selected state families (e.g., in state discrimination).
Are such N-POVMs physically realizable? We give a constructive quantum simulation: for a given N-POVM we build a quantum POVM with a failure outcome whose success-conditioned statistics reproduce the N-POVM on an implementation domain. The simulation has two distinct costs—post-selection (success probability) and domain restriction, interpreted as prior information about admissible states—yet the domain can still contain the families exhibiting an N-POVM advantage, so the separation from POVMs persists under the constraints of the implementation. This provides a quantitative bridge between convex operational theories and quantum mechanics.