Constructing valid density matrices on an NMR quantum information processor via maximum likelihood estimation

TL;DR

This paper demonstrates the use of maximum likelihood estimation to reliably reconstruct valid, positive semi-definite density matrices in NMR quantum information experiments, improving upon standard methods.

Contribution

The authors experimentally implement a maximum likelihood estimation protocol to ensure physically valid quantum state reconstruction on an NMR processor, addressing issues of non-positivity in naive methods.

Findings

Maximum likelihood estimation guarantees positive semi-definite density matrices.

The method outperforms standard state estimation techniques.

Experimental validation on an NMR quantum processor confirms effectiveness.

Abstract

Estimation of quantum states is one of the most important steps in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not positive, and hence not physically acceptable. How do we ensure that at all stages of reconstruction, we keep the density matrix positive and normalized? Recently a method has been suggested based on maximum likelihood estimation, wherein the density matrix is guaranteed to be positive definite. We experimentally implement this protocol and demonstrate its utility on an NMR quantum information processor. We discuss several examples where we undertake such an estimation and compare it with the standard method of state estimation.