Entanglement-enabled advantage for learning a bosonic random displacement channel
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arXiv
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| Format: | Preprint |
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2024
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| author | Oh, Changhun Chen, Senrui Wong, Yat Zhou, Sisi Huang, Hsin-Yuan Nielsen, Jens A. H. Liu, Zheng-Hao Neergaard-Nielsen, Jonas S. Andersen, Ulrik L. Jiang, Liang Preskill, John |
| author_facet | Oh, Changhun Chen, Senrui Wong, Yat Zhou, Sisi Huang, Hsin-Yuan Nielsen, Jens A. H. Liu, Zheng-Hao Neergaard-Nielsen, Jonas S. Andersen, Ulrik L. Jiang, Liang Preskill, John |
| contents | 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. On the other hand, we present a simple entanglement-assisted scheme that only requires a number of samples independent of $n$, given a sufficient amount of squeezing. 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 continuous-variable systems and points toward experimentally feasible demonstrations of provable entanglement-enabled advantage using CV quantum platforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entanglement-enabled advantage for learning a bosonic random displacement channel Oh, Changhun Chen, Senrui Wong, Yat Zhou, Sisi Huang, Hsin-Yuan Nielsen, Jens A. H. Liu, Zheng-Hao Neergaard-Nielsen, Jonas S. Andersen, Ulrik L. Jiang, Liang Preskill, John Quantum Physics 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. On the other hand, we present a simple entanglement-assisted scheme that only requires a number of samples independent of $n$, given a sufficient amount of squeezing. 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 continuous-variable systems and points toward experimentally feasible demonstrations of provable entanglement-enabled advantage using CV quantum platforms. |
| title | Entanglement-enabled advantage for learning a bosonic random displacement channel |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.18809 |