Normalization procedure for relaxation studies in NMR quantum information processing

TL;DR

This paper introduces a normalization method for NMR quantum information processing that accounts for relaxation effects, improving the accuracy of density matrix comparisons over time.

Contribution

It proposes a novel time-dependent normalization procedure for relaxation studies in NMR quantum computing, addressing issues with traditional fixed normalization methods.

Findings

The method accurately tracks purity loss during relaxation.

Application to pseudo-entangled states reveals phenomena like sudden death.

Analysis of pseudo-cat states' Wigner functions demonstrates the method's effectiveness.

Abstract

NMR quantum information processing studies rely on the reconstruction of the density matrix representing the so-called pseudo-pure states (PPS). An initially pure part of a PPS state undergoes unitary and non-unitary (relaxation) transformations during a computation process, causing a "loss of purity" until the equilibrium is reached. Besides, upon relaxation, the nuclear polarization varies in time, a fact which must be taken into account when comparing density matrices at different instants. Attempting to use time-fixed normalization procedures when relaxation is present, leads to various anomalies on matrices populations. On this paper we propose a method which takes into account the time-dependence of the normalization factor. From a generic form for the deviation density matrix an expression for the relaxing initial pure state is deduced. The method is exemplified with an experiment of relaxation of the concurrence of a pseudo-entangled state, which exhibits the phenomenon of sudden death, and the relaxation of the Wigner function of a pseudo-cat state.