June 2019

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Author:
David Collins
Body:

The issue of optimally estimating parameters associated with quantum channels has been thoroughly studied in various contexts, yielded an enhancement of accuracy using resources such as entangled states. For various qubit channels, using the quantum Fisher information per channel invocation as a measure of the estimation accuracy, optimal estimation protocols and the possible advantages that they might yield are well understood. However, these resulting optimal estimation protocols usually require pure initial states. The question remains as to what advantages can be attained when the available initial states are not pure. These have been investigated for some qubit channels with results that differ from those of the pure state cases. 

We consider qubit channel parameter estimation when the available initial states are mixed with very low initial purity, r. We compare two protocols: one where the input states into the channel are uncorrelated states generated 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 for the cases where the channel is invoked on one out of n qubits and whenever the purity satisfies r <<1/sqrt(n). We show that for unital channels the correlated state protocol enhances the quantum Fisher information by a factor between n and n-1 and provide a measurement scheme which yields a classical Fisher information providing the same enhancement. 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. 

 
 
 
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