Estimation of n non-identical unitary channels

TL;DR

This paper studies the simultaneous estimation of multiple non-identical unitary channels using entanglement, showing that entanglement does not improve estimation rates unless channels depend on a common variable.

Contribution

It demonstrates that multi-partite entanglement does not enhance estimation rates for independent channels, but can improve when channels depend on a shared parameter.

Findings

Entanglement does not improve estimation for independent channels.

Entanglement accelerates estimation when channels share a common variable.

The study clarifies conditions under which entanglement benefits parameter estimation.

Abstract

We investigate the simultaneous estimation of $n$ not necessarily identical unitary channels using multi-partite entanglement. We examine whether it is possible for the rate at which the mean square error decreases to be greater than that using the channels individually. For a reasonably general situation, in which there is no functional dependence between the channels, we show that this is not possible. We look at a case in which the channels are not necessarily identical but depend on a common variable. In this case, the mean square error decreases more rapidly using multi-partite entanglement.