Noisy initial-state qubit-channel metrology with additional undesirable noisy evolution

• URL: http://arxiv.org/abs/2412.12085v1
• Date: Mon, 16 Dec 2024 18:55:45 GMT
• Title: Noisy initial-state qubit-channel metrology with additional undesirable noisy evolution
• Authors: David Collins, Taylor Larrechea,
• Abstract summary: We consider protocols for estimating the parameter in a unital qubit channel.<n>We compare two protocols: one uses $n$ qubits prepared in a particular correlated input state and subsequently invokes the channel on one qubit.<n>We show that for certain types of noisy evolution the $n$-qubit protocol will be inferior but for others it will be superior.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider protocols for estimating the parameter in a single-parameter unital qubit channel, assuming that the available initial states are highly mixed with very low purity. We compare two protocols: one uses $n$ qubits prepared in a particular correlated input state and subsequently invokes the channel on one qubit. The other uses a single qubit and invokes the channel once. We compare the accuracy of the protocols using the quantum Fisher information for each. We extend the results of Collins [1] by allowing for additional noisy evolution on the spectator qubits in the $n$-qubit protocol. We provide simple algebraic expressions that will determine when the $n$-qubit protocol is superior and provide techniques that can alleviate certain types of noise. We show that for certain types of noisy evolution the $n$-qubit protocol will be inferior but for others it will be superior.

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