Published December 6, 2024 | Published
Journal Article Open

Entanglement-Enabled Advantage for Learning a Bosonic Random Displacement Channel

  • 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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Additional details

Created:
February 20, 2025
Modified:
February 20, 2025