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
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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)