Estimation of two-qubit interactions through channels with environment assistance

TL;DR

This paper investigates how to optimally estimate two-qubit interactions in a quantum channel model with environment assistance, revealing that environment assistance always helps but entanglement does not improve estimation.

Contribution

It introduces a model for two-qubit interaction estimation with environment assistance and derives optimal strategies, showing environment assistance's universal benefit.

Findings

Environment assistance always improves estimation accuracy.

Entanglement at input does not enhance estimation.

Exact solutions are provided for single-parameter cases on the tetrahedral parameter space.

Abstract

We consider the estimation of two-qubit interactions when initial states of both qubit can be locally controlled, while the final state of only one qubit can be measured. This amounts to realize a model of quantum channel communication with environment assistance. In such a framework the unitaries' parameters space results a tetrahedron in $\mathbb{R}^3$. On its edges the problem, becoming of single parameter estimation, can be exactly solved and we derive optimal probe states and estimators. Our results show that the possibility of environment assistance is always beneficial, while the usage of entanglement at channels' input is not.