State determination: an iterative algorithm

TL;DR

This paper introduces an efficient iterative algorithm for quantum state determination using probability distributions of observables, which converges to the true state or a Pauli partner, aiding in quantum state reconstruction and analysis.

Contribution

The paper presents a novel iterative algorithm based on the Physical Imposition Operator for accurate quantum state reconstruction from observable distributions.

Findings

Algorithm converges to the true state or Pauli partner.

Numerical tests demonstrate efficiency and robustness.

Tool aids in studying Pauli partners and quantum state determination.

Abstract

An iterative algorithm for state determination is presented that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state $\Phi$. Starting form an arbitrary state $\Psi_{0}$, a succession of states $\Psi_{n}$ is obtained that converges to $\Phi$ or to a Pauli partner. This algorithm for state reconstruction is efficient and robust as is seen in the numerical tests presented and is a useful tool not only for state determination but also for the study of Pauli partners. Its main ingredient is the Physical Imposition Operator that changes any state to have the same physical properties, with respect to an observable, of another state.