Robust generalized quantum Stein's lemma
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914571226185728 |
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| author | Mazzola, Giulia Sutter, David Renner, Renato |
| author_facet | Mazzola, Giulia Sutter, David Renner, Renato |
| contents | The generalized quantum Stein's lemma provides an explicit expression for the optimal error exponent when distinguishing many independent and identically distributed (iid) copies of a given bipartite state from the set of separable bipartite states. Here we prove that this result is robust, in the sense that the iid assumption can be relaxed to almost-iid. In particular, our result shows that the original argument of Brandão and Plenio, which contains a logical gap, can be made rigorous. Our proof relies on a novel continuity bound for the relative entropy of entanglement with respect to the quantum Wasserstein distance. Combined with a recent insight that almost-iid states and their exact iid counterparts are asymptotically close in this distance, the bound implies that their relative entropies of entanglement coincide asymptotically. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_16500 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust generalized quantum Stein's lemma Mazzola, Giulia Sutter, David Renner, Renato Quantum Physics The generalized quantum Stein's lemma provides an explicit expression for the optimal error exponent when distinguishing many independent and identically distributed (iid) copies of a given bipartite state from the set of separable bipartite states. Here we prove that this result is robust, in the sense that the iid assumption can be relaxed to almost-iid. In particular, our result shows that the original argument of Brandão and Plenio, which contains a logical gap, can be made rigorous. Our proof relies on a novel continuity bound for the relative entropy of entanglement with respect to the quantum Wasserstein distance. Combined with a recent insight that almost-iid states and their exact iid counterparts are asymptotically close in this distance, the bound implies that their relative entropies of entanglement coincide asymptotically. |
| title | Robust generalized quantum Stein's lemma |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.16500 |