Quantum tomography via Non-orthogonal basis and weak values

TL;DR

This paper introduces a quantum tomography method leveraging non-orthogonal bases and weak values, providing an explicit reconstruction formula analogous to mutually unbiased bases, demonstrated with a qubit example.

Contribution

It presents a novel quantum tomography approach using bi-orthogonal equiseparable bases and weak values, connecting measurement probabilities with basis separation.

Findings

Derived an explicit tomographic reconstruction formula

Established a relationship between weak values and basis separation

Demonstrated method with a qubit example

Abstract

Using a relation between a bi-orthogonal set of equiseparable bases and the weak values of the density matrix we derive an explicit formula for its tomographic reconstruction completely analogous to the standard mutually unbiased bases expansion. With the simple example of a qubit is evidenced the relationship between weak values, measured probabilities and the separation between non-orthogonal bases.