Rescuing complementarity with little drama

Journal of High Energy Physics, Dec 2016

The AMPS paradox challenges black hole complementarity by apparently constructing a way for an observer to bring information from the outside of the black hole into its interior if there is no drama at its horizon, making manifest a violation of monogamy of entanglement. We propose a new resolution to the paradox: this violation cannot be explicitly checked by an infalling observer in the finite proper time they have to live after crossing the horizon. Our resolution depends on a weak relaxation of the no-drama condition (we call it “little-drama”) which is the “complementarity dual” of scrambling of information on the stretched horizon. When translated to the description of the black hole interior, this implies that the fine-grained quantum information of infalling matter is rapidly diffused across the entire interior while classical observables and coarse-grained geometry remain unaffected. Under the assumption that information has diffused throughout the interior, we consider the difficulty of the information-theoretic task that an observer must perform after crossing the event horizon of a Schwarzschild black hole in order to verify a violation of monogamy of entanglement. We find that the time required to complete a necessary subroutine of this task, namely the decoding of Bell pairs from the interior and the late radiation, takes longer than the maximum amount of time that an observer can spend inside the black hole before hitting the singularity. Therefore, an infalling observer cannot observe monogamy violation before encountering the singularity.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2FJHEP12%282016%29026.pdf

Rescuing complementarity with little drama

Received: August Rescuing complementarity with little drama Ning Bao 0 1 4 Adam Bouland 0 1 2 Aidan Chatwin-Davies 0 1 4 Jason Pollack 0 1 4 Henry Yuen 0 1 3 Massachusetts Avenue 0 1 Cambridge 0 1 U.S.A. 0 1 Berkeley 0 1 U.S.A. 0 1 0 Open Access , c The Authors 1 1200 East California Boulevard , Pasadena , U.S.A 2 Computer Science and Arti cial Intelligence Laboratory, Massachusetts Institute of Technology 3 Computer Science Division, University of California , Berkeley 4 Walter Burke Institute for Theoretical Physics, California Institute of Technology The AMPS paradox challenges black hole complementarity by apparently constructing a way for an observer to bring information from the outside of the black hole into its interior if there is no drama at its horizon, making manifest a violation of monogamy of entanglement. We propose a new resolution to the paradox: this violation cannot be explicitly checked by an infalling observer in the nite proper time they have to live after crossing the horizon. Our resolution depends on a weak relaxation of the no-drama condition (we call it \little-drama") which is the \complementarity dual" of scrambling of information on the stretched horizon. When translated to the description of the black hole interior, this ne-grained quantum information of infalling matter is rapidly di used across the entire interior while classical observables and coarse-grained geometry remain una ected. Under the assumption that information has di used throughout the interior, we consider the di culty of the information-theoretic task that an observer must perform after crossing the event horizon of a Schwarzschild black hole in order to verify a violation of monogamy of entanglement. We nd that the time required to complete a necessary subroutine of this task, namely the decoding of Bell pairs from the interior and the late radiation, takes longer than the maximum amount of time that an observer can spend inside the black hole before hitting the singularity. Therefore, an infalling observer cannot observe monogamy violation before encountering the singularity. ArXiv ePrint: 1607.05141 Black Holes; Models of Quantum Gravity 1 Introduction Background: black holes and scrambling Hawking radiation and scrambling: what Alice sees 2 Scrambling, inside and out Scrambling and kinematics Computation behind the horizon Model for verifying entanglement Alice's computational task Modeling scrambling dynamics Black holes in other dimensions Localization of the experimenter Relation to prior works Other black hole geometries The information paradox [1] and its more modern AMPS incarnation [2, 3] are deeply puzzling issues lying at the center of any attempts at reconciling quantum mechanics with gravity. Black hole complementarity, as proposed by [4], attempted to resolve the information paradox by asserting that information that falls into the black hole interior is also retained at the stretched horizon. Observers are only able to access this information in one of two \complementary" descriptions, either in the interior or at the horizon, so that the apparent violation of the no-cloning theorem visible in a global description could never be veri ed. AMPS, however, considered a scenario in which an observer rst collects information on the outside by gathering Hawking radiation, then jumps through the horizon and into the black hole interior. Assuming standard postulates of black hole 2. the validity of low-energy e ective eld theory outside the stretched horizon, 3. that the black hole is a quantum mechanical system with dimension given by eA=4, 4. that the horizon is not a special place | that \no drama" happens at the horizon, so an observer can actually enter the black hole interior, AMPS pointed out an apparent violation of monogamy of entanglement1 among three systems: the black hole interior, the recently emitted Hawking radiation (late radiation), and the previously emitted Hawking radiation (early radiation). To avoid this violation, it therefore seemed necessary to give up one of the assumptions mentioned above, all of which are cherished pillars of modern physics. Giving up the nal assumption would mean that observers who attempt to enter the black hole would be violently destroyed by high-energy excitations, hence the name \ rewall paradox." urry of attempts to resolve the paradox by weakening one or more of the core axioms, or by changing the paradigm completely [5{14]. Reaching consensus as to which resolution is the correct one has proven challenging. An interesting proposed resolution to the information paradox, based on arguments from computational complexity, was given by Harlow and Hayden [15]. They argued that the part of the AMPS experiment where the experimenter has to decode2 entanglement between the old radiation and the late radiation of the black hole involves an extremely difcult computational task. Under very plausible conjectures in computational complexity,3 th (...truncated)


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP12%282016%29026.pdf

Ning Bao, Adam Bouland, Aidan Chatwin-Davies. Rescuing complementarity with little drama, Journal of High Energy Physics, 2016, pp. 26, Volume 2016, Issue 12, DOI: 10.1007/JHEP12(2016)026