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Published December 6, 2024 | Version Published
Journal Article Open

Entanglement-Enabled Advantage for Learning a Bosonic Random Displacement Channel

Creators

  • 1. ROR icon Korea Advanced Institute of Science and Technology
  • 2. ROR icon Perimeter Institute
  • 3. ROR icon California Institute of Technology
  • 4. ROR icon Technical University of Denmark

Abstract

We show that quantum entanglement can provide an exponential advantage in learning properties of a bosonic continuous-variable (CV) system. The task we consider is estimating a probabilistic mixture of displacement operators acting on 𝑛 bosonic modes, called a random displacement channel. We prove that if the 𝑛 modes are not entangled with an ancillary quantum memory, then the channel must be sampled a number of times exponential in 𝑛 in order to estimate its characteristic function to reasonable precision; this lower bound on sample complexity applies even if the channel inputs and measurements performed on channel outputs are chosen adaptively or have unrestricted energy. On the other hand, we present a simple entanglement-assisted scheme that only requires a number of samples independent of 𝑛 in the large squeezing and noiseless limit. This establishes an exponential separation in sample complexity. We then analyze the effect of photon loss and show that the entanglement-assisted scheme is still significantly more efficient than any lossless entanglement-free scheme under mild experimental conditions. Our work illuminates the role of entanglement in learning CV systems and points toward experimentally feasible demonstrations of provable entanglement-enabled advantage using CV quantum platforms.

Copyright and License

© 2024 American Physical Society.

Acknowledgement

We thank Mankei Tsang, Yuxin Wang, Ronald de Wolf, Mingxing Yao, and Ming Yuan for insightful discussions. C. O., S. C., Y. W., and L. J. acknowledge support from the ARO (W911NF-23-1-0077), ARO MURI (W911NF-21-1-0325), AFOSR MURI (FA9550-19-1-0399, FA9550-21-1-0209), NSF (OMA-1936118, ERC-1941583, OMA-2137642), NTT Research, Packard Foundation (2020-71479). J. P. acknowledges support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research (DE-NA0003525, DE-SC0020290), the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center. S. Z. acknowledges funding provided by the Institute for Quantum Information and Matter and Perimeter Institute for Theoretical Physics, a research institute supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. J. A. H. N., Z.-H. L., J. S. N.-N., and U. L. A acknowledge support from DNRF (bigQ, DNRF142), IFD (PhotoQ, 1063-00046A), EU (CLUSTEC, ClusterQ ERC-101055224, GTGBS MC-416 101106833) and NNF (CBQS, 24SA0088433). C. O. acknowledges support from Quantum Technology R&D Leading Program (Quantum Computing) (RS-2024-00431768) through the National Research Foundation of Korea (NRF) funded by the Korean government [Ministry of Science and ICT (MSIT)].

Supplemental Material

Supplemental material contains the derivation of output probabilities for various learning schemes appearing in the main text and a proof of the main theorems.

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PhysRevLett.133.230604.pdf

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Additional details

Funding

United States Army Research Office
W911NF-23-1-0077
Multidisciplinary University Research Initiative
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
OMA-1936118
National Science Foundation
ERC-1941583
National Science Foundation
OMA-2137642
NTT Research
David and Lucile Packard Foundation
2020-71479
United States Department of Energy
DE-NA0003525
United States Department of Energy
DE-SC0020290
Office of Science
Institute for Quantum Information and Matter, California Institute of Technology
Perimeter Institute
Government of Canada
Innovation, Science and Economic Development Canada
Ministry of Colleges and Universities
Danish National Research Foundation
DNRF142
Danish National Research Foundation
1063-00046A
European Research Council
CLUSTEC
European Research Council
ClusterQ ERC-101055224
European Research Council
GTGBS MC-101106833
National Research Foundation of Korea
Ministry of Science and ICT
NSF Physics Frontiers Center
Province of Ontario
Quantum Technology R&D Leading Program
RS-2024-00431768

Dates

Accepted
2024-10-29
Accepted
Available
2024-12-06
Published online

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Caltech groups
Institute for Quantum Information and Matter
Publication Status
Published