Maximally entangled states are not always useful for single shot distinguishability of unitaries
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911316260683776 |
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| author | Manna, Satyaki Bhowmik, Anandamay Das Saha, Debashis |
| author_facet | Manna, Satyaki Bhowmik, Anandamay Das Saha, Debashis |
| contents | There have been many instances where the maximally entangled state as a probe acts better than the product and the non-maximally entangled states in the task of distinguishing quantum channels. We provide a proof that for single-shot discrimination of two unitary channels, entangled and product states are operationally equivalent. But we identify pairs of unitaries that are perfectly distinguishable using a non-maximally entangled state, but not with a maximally entangled one. This contrast becomes more pronounced when the number of unitaries exceeds two. In every dimension $\geqslant 3$, we show that there exists a class of unitaries that are indistinguishable under maximally entangled probes, yet perfectly distinguishable using product or non-maximally entangled inputs. Another interesting set of unitaries in every dimension $\geqslant 3$ has been presented where only non-maximally entangled state acts as the successful probe, while product states and maximally entangled states cannot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximally entangled states are not always useful for single shot distinguishability of unitaries Manna, Satyaki Bhowmik, Anandamay Das Saha, Debashis Quantum Physics There have been many instances where the maximally entangled state as a probe acts better than the product and the non-maximally entangled states in the task of distinguishing quantum channels. We provide a proof that for single-shot discrimination of two unitary channels, entangled and product states are operationally equivalent. But we identify pairs of unitaries that are perfectly distinguishable using a non-maximally entangled state, but not with a maximally entangled one. This contrast becomes more pronounced when the number of unitaries exceeds two. In every dimension $\geqslant 3$, we show that there exists a class of unitaries that are indistinguishable under maximally entangled probes, yet perfectly distinguishable using product or non-maximally entangled inputs. Another interesting set of unitaries in every dimension $\geqslant 3$ has been presented where only non-maximally entangled state acts as the successful probe, while product states and maximally entangled states cannot. |
| title | Maximally entangled states are not always useful for single shot distinguishability of unitaries |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.14499 |