Conditional SIC-POVMs

TL;DR

This paper introduces the concept of conditional SIC-POVMs, a generalization of SIC-POVMs tailored for scenarios where some parameters of the quantum state are known, focusing on cases with known diagonal elements.

Contribution

It defines and analyzes the existence of conditional SIC-POVMs, especially when the density matrix's diagonal elements are known, extending the theory of quantum measurements.

Findings

Conditional SIC-POVMs are characterized for known diagonal cases.

Existence results are provided for specific scenarios.

The concept extends optimal quantum measurements for partial state knowledge.

Abstract

In this paper we examine a generalization of the symmetric informationally complete POVMs. SIC-POVMs are the optimal measurements for full quantum tomography, but if some parameters of the density matrix are known, then the optimal SIC POVM should be orthogonal to a subspace. This gives the concept of the conditional SIC-POVM. The existence is not known in general, but we give a result in the special cases when the diagonal is known of the density matrix.