2016/10/31 by Shira Chapman, Hugo Marrochio, Robert C. Myers
Physics and Astronomy · #hep-th #gr-qc #quant-ph
paper · pdf · doi:10.1007/jhep01(2017)062
published as JHEP 1701 (2017) 062 · 37+32 pages, 24 figures; v2 - added appendix (Insights from MERA), added references, corrected typos
arxiv created 2016/11/17 · arxiv updated 2017/06/15
It was recently conjectured that the quantum complexity of a holographic boundary state can be computed by evaluating the gravitational action on a bulk region known as the Wheeler-DeWitt patch. We apply this complexity=action duality to evaluate the `complexity of formation' (arXiv:1509.07876, arXiv:1512.04993), i.e., the additional complexity arising in preparing the entangled thermofield double state with two copies of the boundary CFT compared to preparing the individual vacuum states of the two copies. We find that for boundary dimensions d>2, the difference in the complexities grows linearly with the thermal entropy at high temperatures. For the special case d=2, the complexity of formation is a fixed constant, independent of the temperature. We compare these results to those found using the complexity=volume duality.