Efficient learning of arbitrary single-copy quantum states
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913811024314368 |
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| author | Roy, Shibdas Caruso, Filippo Patil, Srushti Mukhopadhyay, Anumita |
| author_facet | Roy, Shibdas Caruso, Filippo Patil, Srushti Mukhopadhyay, Anumita |
| contents | Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum state of the experiment, because an exponentially high number of copies of the state is required. In this work, we present an efficient algorithm to estimate with a small but non-zero probability of error the output state of the experiment using a single copy of the state, without knowing the evolution dynamics of the state. It also does not destroy the original state, which can be recovered easily for any further quantum processing. As an example, it is usually required to repeat a quantum image processing experiment many times, since many copies of the state of the output image are needed to extract the information from all its pixels. The information from $\mathcal{N}$ pixels of the image can be inferred from a single run of the image processing experiment in our algorithm, to efficiently estimate the density matrix of the image state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19748 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient learning of arbitrary single-copy quantum states Roy, Shibdas Caruso, Filippo Patil, Srushti Mukhopadhyay, Anumita General Physics Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum state of the experiment, because an exponentially high number of copies of the state is required. In this work, we present an efficient algorithm to estimate with a small but non-zero probability of error the output state of the experiment using a single copy of the state, without knowing the evolution dynamics of the state. It also does not destroy the original state, which can be recovered easily for any further quantum processing. As an example, it is usually required to repeat a quantum image processing experiment many times, since many copies of the state of the output image are needed to extract the information from all its pixels. The information from $\mathcal{N}$ pixels of the image can be inferred from a single run of the image processing experiment in our algorithm, to efficiently estimate the density matrix of the image state. |
| title | Efficient learning of arbitrary single-copy quantum states |
| topic | General Physics |
| url | https://arxiv.org/abs/2310.19748 |