Consistent assignment of quantum probabilities

TL;DR

This paper addresses the problem of assigning quantum probabilities consistently across different measurement bases, providing an optimal solution and exploring implications for quantum state tomography and secret sharing.

Contribution

It introduces a novel method for consistent probability assignment in quantum measurements and demonstrates its optimality, extending the understanding of quantum probability frameworks.

Findings

Optimal solution for consistent quantum probability assignment

Implications for quantum state tomography

Potential applications in quantum secret sharing

Abstract

We pose and solve a problem concerning consistent assignment of quantum probabilities to a set of bases associated with maximal projective measurements. We show that our solution is optimal. We also consider some consequences of the main theorem in the paper in conjunction with Gleason's theorem. Some potential applications to state tomography and probabilistic quantum secret-sharing scheme are discussed.