Triangle Criterion: a mixed-state magic criterion with applications in distillation and detection
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918456034590720 |
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| author | Liu, Zhenhuan Haug, Tobias Ye, Qi Liu, Zi-Wen Roth, Ingo |
| author_facet | Liu, Zhenhuan Haug, Tobias Ye, Qi Liu, Zi-Wen Roth, Ingo |
| contents | We introduce a mixed-state magic criterion, the Triangle Criterion, which plays a role for magic analogous to the Positive Partial Transposition (PPT) Criterion for entanglement: it combines strong detection capability, a clear geometric interpretation, and an operational link to magic distillation. Using this criterion, we uncover several new features of multi-qubit magic distillation and detection. We prove that genuinely multi-qubit magic distillation protocols are strictly more powerful than all single-qubit schemes by showing that the Triangle Criterion is not stable under tensor products. Moreover, we show that, with overwhelming probability, multi-qubit magic states with relatively low rank cannot be distilled by any single-qubit distillation protocol. We derive an upper bound on the minimal purity of magic states, which is conjectured to be tight with both numerical and constructive evidences. Using this minimal-purity result, we predict the existence of unfaithful magic states, namely states that cannot be detected by any fidelity-based magic witness, and reveal fundamental limitations of mixed-state magic detection in any single-copy scheme. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_16777 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Triangle Criterion: a mixed-state magic criterion with applications in distillation and detection Liu, Zhenhuan Haug, Tobias Ye, Qi Liu, Zi-Wen Roth, Ingo Quantum Physics We introduce a mixed-state magic criterion, the Triangle Criterion, which plays a role for magic analogous to the Positive Partial Transposition (PPT) Criterion for entanglement: it combines strong detection capability, a clear geometric interpretation, and an operational link to magic distillation. Using this criterion, we uncover several new features of multi-qubit magic distillation and detection. We prove that genuinely multi-qubit magic distillation protocols are strictly more powerful than all single-qubit schemes by showing that the Triangle Criterion is not stable under tensor products. Moreover, we show that, with overwhelming probability, multi-qubit magic states with relatively low rank cannot be distilled by any single-qubit distillation protocol. We derive an upper bound on the minimal purity of magic states, which is conjectured to be tight with both numerical and constructive evidences. Using this minimal-purity result, we predict the existence of unfaithful magic states, namely states that cannot be detected by any fidelity-based magic witness, and reveal fundamental limitations of mixed-state magic detection in any single-copy scheme. |
| title | Triangle Criterion: a mixed-state magic criterion with applications in distillation and detection |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.16777 |