Abstract
In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy takes non-negative real values and is bounded by the logarithm of the Hilbert space dimensions. The SVD entanglement entropy can be interpreted as the average number of Bell pairs distillable from intermediates states. We observe that the SVD entanglement entropy gets enhanced when the two states are in the different quantum phases in an explicit example of the transverse-field Ising model. Moreover, we calculate the Rényi SVD entropy in various field theories and examine holographic calculations using the AdS/CFT correspondence.
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Acknowledgments
We are grateful to James Fullwood, Dongsheng Ge, Jonathan Harper, Zhian Jia, Ali Mollabashi, Yoshifumi Nakata, Pratik Nandy, Shinsei Ryu, and Aephraim Steinberg for discussions.
This work is supported by the Simons Foundation through the “It from Qubit” and by MEXT KAKENHI Grant-in-Aid for Transformative Research Areas (A) through the “Extreme Universe” collaboration: Grant Number 21H05182, 21H05183 and 21H05187. This work is also supported by Inamori Research Institute for Science and by JSPS Grant-in-Aid for Scientific Research (A) No. 21H04469. The work of YT is supported by Grant-in-Aid for JSPS Fellows No. 22J21950, No. 22KJ1971. ZW was supported by Grant-in-Aid for JSPS Fellows No. 20J23116.
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Parzygnat, A.J., Takayanagi, T., Taki, Y. et al. SVD entanglement entropy. J. High Energ. Phys. 2023, 123 (2023). https://doi.org/10.1007/JHEP12(2023)123
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DOI: https://doi.org/10.1007/JHEP12(2023)123