21 research outputs found
Holograms In Our World
In AdS/CFT, the entanglement wedge EW is the portion of the bulk
geometry that can be reconstructed from a boundary region ; in other words,
EW is the hologram of . We extend this notion to arbitrary spacetimes.
Given any gravitating region , we define a max- and a min-entanglement
wedge, and , such that .
Unlike their analogues in AdS/CFT, these two spacetime regions can differ
already at the classical level, when the generalized entropy is approximated by
the area. All information outside in can flow inwards
towards , through quantum channels whose capacity is controlled by the areas
of intermediate homology surfaces. In contrast, all information outside can flow outwards.
The generalized entropies of appropriate entanglement wedges obey strong
subadditivity, suggesting that they represent the von Neumann entropies of
ordinary quantum systems. The entanglement wedges of suitably independent
regions satisfy a no-cloning relation. This suggests that it may be possible
for an observer in to summon information from spacelike related points in
, using resources that transcend the semiclassical description
of .Comment: 26 pages, 5 figure
Entanglement Wedges for Gravitating Regions
Motivated by properties of tensor networks, we conjecture that an arbitrary
gravitating region can be assigned a generalized entanglement wedge
, such that quasi-local operators in have a holographic
representation in the full algebra generated by quasi-local operators in .
The universe need not be asymptotically flat or AdS, and need not be
asymptotic or weakly gravitating.
On a static Cauchy surface , we propose that is the superset of
that minimizes the generalized entropy. We prove that satisfies a
no-cloning theorem and appropriate forms of strong subadditivity and nesting.
If lies near a portion of the conformal boundary of AdS, our proposal
reduces to the Quantum Minimal Surface prescription applied to . We also
discuss possible covariant extensions of this proposal, such as the smallest
generalized entropy quantum normal superset of .
Our results are consistent with the conjecture that information in that
is spacelike to in the semiclassical description can nevertheless be
recovered from , by microscopic operators that break that description. We
thus propose that quantifies the range of holographic encoding, an
important nonlocal feature of quantum gravity, in general spacetimes.Comment: 26 pages, 11 figure
Leading order corrections to the quantum extremal surface prescription
We show that a na\"{i}ve application of the quantum extremal surface (QES)
prescription can lead to paradoxical results and must be corrected at leading
order. The corrections arise when there is a second QES (with strictly larger
generalized entropy at leading order than the minimal QES), together with a
large amount of highly incompressible bulk entropy between the two surfaces. We
trace the source of the corrections to a failure of the assumptions used in the
replica trick derivation of the QES prescription, and show that a more careful
derivation correctly computes the corrections. Using tools from one-shot
quantum Shannon theory (smooth min- and max-entropies), we generalize these
results to a set of refined conditions that determine whether the QES
prescription holds. We find similar refinements to the conditions needed for
entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted
as the task of one-shot quantum state merging (using zero-bits rather than
classical bits), a task gravity is able to achieve optimally efficiently.Comment: 87 pages, 9 figures, 4 appendices; v2 fixed typo
Large N algebras and generalized entropy
We construct a Type II von Neumann algebra that describes the large
physics of single-trace operators in AdS/CFT in the microcanonical
ensemble, where there is no need to include perturbative corrections.
Using only the extrapolate dictionary, we show that the entropy of
semiclassical states on this algebra is holographically dual to the generalized
entropy of the black hole bifurcation surface. From a boundary perspective,
this constitutes a derivation of a special case of the QES prescription without
any use of Euclidean gravity or replicas; from a purely bulk perspective, it is
a derivation of the quantum-corrected Bekenstein-Hawking formula as the entropy
of an explicit algebra in the limit of Lorentzian effective field
theory quantum gravity. In a limit where a black hole is first allowed to
equilibrate and then is later potentially re-excited, we show that the
generalized second law is a direct consequence of the monotonicity of the
entropy of algebras under trace-preserving inclusions. Finally, by considering
excitations that are separated by more than a scrambling time we construct a
"free product" von Neumann algebra that describes the semiclassical physics of
long wormholes supported by shocks. We compute R\'{e}nyi entropies for this
algebra and show that they are equal to a sum over saddles associated to
quantum extremal surfaces in the wormhole. Surprisingly, however, the saddles
associated to "bulge" quantum extremal surfaces contribute with a negative
sign.Comment: 57 pages + appendice
Fun with replicas: tripartitions in tensor networks and gravity
We introduce a new correlation measure for tripartite pure states that we
call . The quantity is symmetric with respect to the subsystems ,
, , invariant under local unitaries, and is bounded from above by . For random tensor network states, we prove that is equal
to the size of the minimal tripartition of the tensor network, i.e., the
logarithmic bond dimension of the smallest cut that partitions the network into
three components with , , and . We argue that for holographic states
with a fixed spatial geometry, is similarly computed by the minimal
area tripartition. For general holographic states, is determined by
the minimal area tripartition in a backreacted geometry, but a smoothed version
is equal to the minimal tripartition in an unbackreacted geometry at leading
order. We briefly discuss a natural family of quantities for
integer that generalize . In holography, the computation of
for spontaneously breaks part of a replica symmetry. This prevents any naive application of the
Lewkowycz-Maldacena trick in a hypothetical analytic continuation to .Comment: 28 pages, 10 figure
Quantum Maximin Surfaces
We formulate a quantum generalization of maximin surfaces and show that a
quantum maximin surface is identical to the minimal quantum extremal surface,
introduced in the EW prescription. We discuss various subtleties and
complications associated to a maximinimization of the bulk von Neumann entropy
due to corners and unboundedness and present arguments that nonetheless a
maximinimization of the UV-finite generalized entropy should be well-defined.
We give the first general proof that the EW prescription satisfies entanglement
wedge nesting and the strong subadditivity inequality. In addition, we apply
the quantum maximin technology to prove that recently proposed generalizations
of the EW prescription to nonholographic subsystems (including the so-called
"quantum extremal islands") also satisfy entanglement wedge nesting and strong
subadditivity. Our results hold in the regime where backreaction of bulk
quantum fields can be treated perturbatively in , but we emphasize
that they are valid even when gradients of the bulk entropy are of the same
order as variations in the area, a regime recently investigated in new models
of black hole evaporation in AdS/CFT.Comment: 52 pages, 9 figures, v2: updated text, v3: fixed typo
One-shot holography
Following the work of [2008.03319], we define a generally covariant
max-entanglement wedge of a boundary region , which we conjecture to be the
bulk region reconstructible from . We similarly define a covariant
min-entanglement wedge, which we conjecture to be the bulk region that can
influence the boundary state on . We prove that the min- and
max-entanglement wedges obey various properties necessary for this conjecture,
such as nesting, inclusion of the causal wedge, and a reduction to the usual
quantum extremal surface prescription in the appropriate special cases. These
proofs rely on one-shot versions of the (restricted) quantum focusing
conjecture (QFC) that we conjecture to hold. We argue that this QFC implies a
one-shot generalized second law (GSL) and quantum Bousso bound. Moreover, in a
particular semiclassical limit we prove this one-shot GSL directly using
algebraic techniques. Finally, in order to derive our results, we extend both
the frameworks of one-shot quantum Shannon theory and state-specific
reconstruction to finite-dimensional von Neumann algebras, allowing nontrivial
centers.Comment: 84 pages, 8 figure
Python’s Lunch: geometric obstructions to decoding Hawking radiation
According to Harlow and Hayden [arXiv:1301.4504] the task of distilling information out of Hawking radiation appears to be computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. We trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, we conjecture a precise formula relating the computational hardness of distilling information to geometric properties of the wormhole — specifically to the exponential of the difference in generalized entropies between the two non-minimal quantum extremal surfaces that constitute the obstruction. Due to its shape, we call this obstruction the ‘Python’s Lunch’, in analogy to the reptile’s postprandial bulge
Python’s Lunch: geometric obstructions to decoding Hawking radiation
According to Harlow and Hayden [arXiv:1301.4504] the task of distilling information out of Hawking radiation appears to be computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. We trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, we conjecture a precise formula relating the computational hardness of distilling information to geometric properties of the wormhole — specifically to the exponential of the difference in generalized entropies between the two non-minimal quantum extremal surfaces that constitute the obstruction. Due to its shape, we call this obstruction the ‘Python’s Lunch’, in analogy to the reptile’s postprandial bulge