Tight Bounds on Pauli Channel Learning without Entanglement
Abstract
Quantum entanglement is a crucial resource for learning properties from nature, but a precise characterization of its advantage can be challenging. In this Letter, we consider learning algorithms without entanglement to be those that only utilize states, measurements, and operations that are separable between the main system of interest and an ancillary system. Interestingly, we show that these algorithms are equivalent to those that apply quantum circuits on the main system interleaved with mid-circuit measurements and classical feedforward. Within this setting, we prove a tight lower bound for Pauli channel learning without entanglement that closes the gap between the best-known upper and lower bound. In particular, we show that Θ(2ⁿϵ⁻²) rounds of measurements are required to estimate each eigenvalue of an n-qubit Pauli channel to ϵ error with high probability when learning without entanglement. In contrast, a learning algorithm with entanglement only needs Θ(ϵ⁻²) copies of the Pauli channel. The tight lower bound strengthens the foundation for an experimental demonstration of entanglement-enhanced advantages for Pauli noise characterization.
Copyright and License
© 2024 American Physical Society.
Acknowledgement
Data Availability
The supplemental PDF file contains additional details about the proof and calculation that support the results stated in the letter.
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PhysRevLett.132.180805.pdf
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Additional details
Identifiers
- ISSN
- 1079-7114
Funding
- United States Army Research Office
- W911NF-23-1-0077
- United States Army Research Office
- W911NF-21-1-0325
- United States Air Force Office of Scientific Research
- FA9550-19-1-0399
- United States Air Force Office of Scientific Research
- FA9550-21-1-0209
- National Science Foundation
- OSI-1936118
- National Science Foundation
- EEC-1941583
- National Science Foundation
- OSI-2137642
- NTT Research
- David and Lucile Packard Foundation
- 2020-71479
- United States Department of Energy
- California Institute of Technology
- Institute for Quantum Information and Matter
- National Science Foundation
- PHY-1733907
- Perimeter Institute
- Ministry of Colleges and Universities
- Government of Ontario
- Ministry of Colleges and Universities
- MediaTek Research Young Scholarship
- Google Ph.D. fellowship
- Massachusetts Institute of Technology