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An alternative to purification in CFT

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arxiv 2406.09033 v1 pith:WMYZYOJU submitted 2024-06-13 hep-th

Xin Jiang , Peng Wang , Houwen Wu , Haitang Yang This is my paper · ORCID
classification hep-th
keywords entanglementstateconstructedemphentropypurepurificationtext
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abstract

In conformal field theories, in contrast to \emph{adding} some auxiliary states into the bipartite mixed state $\rho_{AB}$ as the usual purifications do, we show a pure entangled state $\psi_{AB}$ can be constructed by \emph{subtracting} the undetectable regions. In this pure state $\psi_{AB}$, 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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exact and Finite de Sitter QFT from CFT

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Constructs exact finite de Sitter QFT from CFT data using moduli space of oriented balls and Casimir completion of operators.

  2. Entanglement Entropy of Mixed State in Thermal CFT$_2$

    hep-th 2025-01 conditional novelty 6.0 of 10

    The paper derives the entanglement entropy of two disjoint intervals in a thermal 2D conformal field theory, identifies its holographic dual as an entanglement wedge cross section in a BTZ black hole, and shows this c...

  3. R\'enyi Entanglement of Purification and Half R\'enyi Reflected Entropy in Free Scalar Theory

    hep-th 2025-01 conditional novelty 5.0 of 10

    In a free scalar lattice model, numerical calculations show Rényi entanglement of purification is at least half the Rényi reflected entropy for 0 < n < 2 in the small subsystems tested.

  4. Mixed state entanglement in deformed field theory at finite temperature

    hep-th 2024-12 conditional novelty 5.0 of 10

    For a TTbar-deformed CFT at finite temperature, the EWCS and holographic entanglement negativity both decrease as the deformation parameter grows, just as they do when temperature increases.

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