Journal article

Entanglement and complexity of purification in (1 1)-dimensional free conformal field theories

Hugo A Camargo, Lucas Hackl, Michal P Heller, Alexander Jahn, Tadashi Takayanagi, Bennet Windt



Finding pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace is necessarily a challenging task. Nevertheless, such purifications play the key role in characterizing quantum information-theoretic properties of mixed states via entanglement and complexity of purifications. In this article, we analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories using the most general Gaussian purifications. We provide a comprehensive comparison with existing results and identify universal properties. We further discuss important subtleties in our setup: the massless limit of the free bosonic theo..

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University of Melbourne Researchers


Awarded by JSPS

Awarded by long-term workshop Quantum Information and String Theory

Funding Acknowledgements

We thank J. Eisert, R. Jefferson, R. Myers, N. Shiba, K. Tamaoka, and K. Umemoto for helpful conversations and J. Knaute, L. Shaposhnik and V. Svensson for comments on the draft. The Gravity, Quantum Fields, and Information group at AEI is supported by the Alexander von Humboldt Foundation and the Federal Ministry for Education and Research through the Sofja Kovalevskaja Award. H.C. is partially supported by the Konrad-Adenauer-Stiftung through their Sponsorship Program for Foreign Students and by the International Max Planck Research School for Mathematical and Physical Aspects of Gravitation, Cosmology, and Quantum Field Theory. A.J. has been supported by the FQXi as well as the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science, and Economic Development and by the Province of Ontario through the Ministry of Research and Innovation. T.T. is supported by Inamori Research Institute for Science and World Premier International Research Center Initiative (WPI Initiative) from the Japan Ministry of Education, Culture, Sports, Science, and Technology (MEXT). T.T. is also supported by JSPS Grant-in-Aid for Scientific Research (A) No. 16H02182 and by JSPS Grant-inAid for Challenging Research (Exploratory) No. 18K18766. We are also grateful to the long-term workshop Quantum Information and String Theory (YITP-T-19-03) held at Yukawa Institute for Theoretical Physics, Kyoto University, where this work was initiated.