Noisy frequency estimation with noisy probes

Górecka, Agnieszka; Pollock, Felix A; Liuzzo-Scorpo, Pietro; Nichols, Rosanna; Adesso, Gerardo; Modi, Kavan

Abstract

We consider frequency estimation in a noisy environment with noisy probes. This builds on previous studies, most of which assume that the initial probe state is pure, while the encoding process is noisy, or that the initial probe state is mixed, while the encoding process is noiseless. Our work is more representative of reality, where noise is unavoidable in both the initial state of the probe and the estimation process itself. We prepare the probe in a GHZ diagonal state, starting from n + 1 qubits in an arbitrary uncorrelated mixed state, and subject it to parameter encoding under dephasing noise. For this scheme, we derive a simple formula for the (quantum and classical) Fisher information, and show that quantum enhancements do not depend on the initial mixedness of the qubits. That is, we show that the so-called 'Zeno' scaling is attainable when the noise present in the encoding process is time inhomogeneous. This scaling does not depend on the mixedness of the initial probe state, and it is retained even for highly mixed states that can never be entangled. We then show that the sensitivity of the probe in our protocol is invariant under permutations of qubits, and monotonic in purity of the initial state of the probe. Finally, we discuss two limiting cases, where purity is either distributed evenly among the probes or concentrated in a single probe.

Citation

Górecka, A., Pollock, F. A., Liuzzo-Scorpo, P., Nichols, R., Adesso, G., & Modi, K. (2018). Noisy frequency estimation with noisy probes. New Journal of Physics, 20(8), Article 083008. https://doi.org/10.1088/1367-2630/aad4e5

• Journal Article Type: Article
• Acceptance Date: Jul 20, 2018
• Online Publication Date: Aug 7, 2018
• Publication Date: Aug 7, 2018
• Deposit Date: Aug 9, 2018
• Publicly Available Date: Aug 9, 2018
• Journal: New Journal of Physics
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 20
• Issue: 8
• Article Number: 083008
• DOI: https://doi.org/10.1088/1367-2630/aad4e5
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/985349
• Publisher URL: http://iopscience.iop.org/article/10.1088/1367-2630/aad4e5/meta
• Additional Information: Journal title: New Journal of Physics; Article type: paper; Article title: Noisy frequency estimation with noisy probes; Copyright information: © 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft; License information: cc-by Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Date received: 2018-04-04; Date accepted: 2018-07-20; Online publication date: 2018-08-07