Abstract
We extend the results of arXiv:2209.12903 by studying local projective measurements performed on subregions of two copies of a CFT2 in the thermofield double state and investigating their consequences on the bulk double-sided black hole holographic dual. We focus on CFTs defined on an infinite line and consider measurements of both finite and semi-infinite subregions. In the former case, the connectivity of the bulk spacetime is preserved after the measurement. In the latter case, the measurement of two semi-infinite intervals in one CFT or of one semi-infinite interval in each CFT can destroy the Einstein-Rosen bridge and disconnect the bulk dual spacetime. In particular, we find that a transition between a connected and disconnected phase occurs depending on the relative size of the measured and unmeasured subregions and on the specific Cardy state the measured subregions are projected on. We identify this phase transition as an entangled/disentangled phase transition of the dual CFT system by computing the post-measurement holographic entanglement entropy between the two CFTs. We also find that bulk information encoded in one CFT in the absence of measurement can sometimes be reconstructed from the other CFT when a measurement is performed, or can be erased by the measurement. Finally, we show that a purely CFT calculation of the Renyi entropy using the replica trick yields results compatible with those obtained in our bulk analysis.
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Acknowledgments
We would like to thank Raphael Bousso, Alexey Milekhin, Vincent Su for helpful discussions. We acknowledge support from the Simons Foundation via It From Qubit (S-K.J.), from the U.S. Department of Energy grant DE-SC0009986 (S-K.J. and B.G.S.), from the AFOSR under FA9550-19-1-0360 (B.G-W.), and from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program “FAR-QC” (S.A.). Part of S.-K.J.’s work is supported by a startup fund at Tulane University.
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Antonini, S., Grado-White, B., Jian, SK. et al. Holographic measurement in CFT thermofield doubles. J. High Energ. Phys. 2023, 14 (2023). https://doi.org/10.1007/JHEP07(2023)014
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DOI: https://doi.org/10.1007/JHEP07(2023)014