Qubit channel parameter estimation with very noisy initial states

Presenting Author: David Collins, Colorado Mesa University

The accuracy of physical processes for estimating parameters associated with single qubit channels depends on the physical systems used to probe the channel, the choices of measurements, processing of measurement outcomes and the choices of probe input states. These can be assessed using the quantum Fisher information per channel invocation as a measure of the estimation accuracy. The resulting optimal estimation protocols usually require that the initial states that are used to generate the input states are pure. We consider qubit channel parameter estimation when the available initial states are mixed with very low initial purity; these occur in situations such as nuclear magnetic resonance (NMR). We compare two protocols: one where the input states into the channel are uncorrelated states generated independently from the individual qubit initial states and the other where the input states are prepared from the same initial states using a particular multi-qubit correlating preparatory unitary. We compare these, in the limit as the purity approaches zero, for the cases where the channel is invoked on one out of n qubits. We show that for unital channels the correlated state protocol enhances the quantum Fisher information by a factor between n and n-1. We also show that for a broad class of non-unital channels, there is no enhancement possible to lowest order in purity, regardless of the input state.

Read this article online: https://arxiv.org/abs/1706.03552

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