An alternative to purification in CFT
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913664950337536 |
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| author | Jiang, Xin Wang, Peng Wu, Houwen Yang, Haitang |
| author_facet | Jiang, Xin Wang, Peng Wu, Houwen Yang, Haitang |
| contents | In conformal field theories, in contrast to \emph{adding} some auxiliary states into the bipartite mixed state $ρ_{AB}$ as the usual purifications do, we show a pure entangled state $ψ_{AB}$ can be constructed by \emph{subtracting} the undetectable regions. In this pure state $ψ_{AB}$, the von Neumann entropy $S_{\text{vN}}(A)$ naturally captures quantum entanglement between $A$ and $B$. We verify that $S_{\text{vN}}(A)$ is equal to the entanglement wedge cross-section $E_{W}$ in AdS spacetime, which is conjectured to be the holographic dual of the entanglement of purification. We show such constructed entanglement entropy has a phase transition. The ordinary entanglement entropies of critical and non-critical QFTs are simply limits of the two phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An alternative to purification in CFT Jiang, Xin Wang, Peng Wu, Houwen Yang, Haitang High Energy Physics - Theory In conformal field theories, in contrast to \emph{adding} some auxiliary states into the bipartite mixed state $ρ_{AB}$ as the usual purifications do, we show a pure entangled state $ψ_{AB}$ can be constructed by \emph{subtracting} the undetectable regions. In this pure state $ψ_{AB}$, the von Neumann entropy $S_{\text{vN}}(A)$ naturally captures quantum entanglement between $A$ and $B$. We verify that $S_{\text{vN}}(A)$ is equal to the entanglement wedge cross-section $E_{W}$ in AdS spacetime, which is conjectured to be the holographic dual of the entanglement of purification. We show such constructed entanglement entropy has a phase transition. The ordinary entanglement entropies of critical and non-critical QFTs are simply limits of the two phases. |
| title | An alternative to purification in CFT |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.09033 |