The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension , knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an\textit {explicit} spacetime metric reconstruction.

1 aBao, Ning1 aCao, ChunJun1 aFischetti, Sebastian1 aKeeler, Cynthia uhttps://arxiv.org/abs/1904.0483401300nas a2200169 4500008004100000245006300041210006300104260001500167300001100182490000700193520081800200100001401018700002001032700002401052700001701076856003701093 2017 eng d00aFast optimization algorithms and the cosmological constant0 aFast optimization algorithms and the cosmological constant c2017/11/13 a1035120 v963 aDenef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of an NP-hard problem. The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10−120 in a randomly generated 109 -dimensional ADK landscape.

1 aBao, Ning1 aBousso, Raphael1 aJordan, Stephen, P.1 aLackey, Brad uhttps://arxiv.org/abs/1706.0850301660nas a2200157 4500008004100000245004900041210004800090260001500138300001100153490000800164520123800172100001401410700001801424700002401442856003601466 2016 eng d00aGrover search and the no-signaling principle0 aGrover search and the nosignaling principle c2016/09/14 a1205010 v1173 aFrom an information processing point of view, two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Here, we investigate the degree to which these two properties are connected. We examine four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox: nonunitary dynamics, non-Born-rule measurement, cloning, and postselection. We find that each model admits superluminal signaling if and only if it admits a query complexity speedup over Grover's algorithm. Furthermore, we show that the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover's algorithm. Hence, one can perform a physically reasonable experiment demonstrating superluminal signaling if and only if one can perform a reasonable experiment inducing a speedup over Grover's algorithm.

1 aBao, Ning1 aBouland, Adam1 aJordan, Stephen, P. uhttp://arxiv.org/abs/1511.00657