10 research outputs found
Holographic Inequalities and Entanglement of Purification
We study the conjectured holographic duality between entanglement of
purification and the entanglement wedge cross-section. We generalize both
quantities and prove several information theoretic inequalities involving them.
These include upper bounds on conditional mutual information and tripartite
information, as well as a lower bound for tripartite information. These
inequalities are proven both holographically and for general quantum states. In
addition, we use the cyclic entropy inequalities to derive a new holographic
inequality for the entanglement wedge cross-section, and provide numerical
evidence that the corresponding inequality for the entanglement of purification
may be true in general. Finally, we use intuition from bit threads to extend
the conjecture to holographic duals of suboptimal purifications.Comment: 17 pages, 4 figures, 1 table. v2: added clarification and fixed typ
Asymptotic Charges Cannot Be Measured in Finite Time
To study quantum gravity in asymptotically flat spacetimes, one would like to
understand the algebra of observables at null infinity. Here we show that the
Bondi mass cannot be observed in finite retarded time, and so is not contained
in the algebra on any finite portion of . This follows
immediately from recently discovered asymptotic entropy bounds. We verify this
explicitly, and we find that attempts to measure a conserved charge at
arbitrarily large radius in fixed retarded time are thwarted by quantum
fluctuations. We comment on the implications of our results to flat space
holography and the BMS charges at .Comment: 9 pages, 3 figures. v2 typos fixed and minor addition
A Density Spike on Astrophysical Scales from an N-Field Waterfall Transition
Hybrid inflation models are especially interesting as they lead to a spike in
the density power spectrum on small scales, compared to the CMB, while also
satisfying current bounds on tensor modes. Here we study hybrid inflation with
waterfall fields sharing a global symmetry. The inclusion of many
waterfall fields has the obvious advantage of avoiding topologically stable
defects for . We find that it also has another advantage: it is easier to
engineer models that can simultaneously (i) be compatible with constraints on
the primordial spectral index, which tends to otherwise disfavor hybrid models,
and (ii) produce a spike on astrophysically large length scales. The latter may
have significant consequences, possibly seeding the formation of
astrophysically large black holes. We calculate correlation functions of the
time-delay, a measure of density perturbations, produced by the waterfall
fields, as a convergent power series in both and the field's correlation
function . We show that for large , the two-point function is
and the
three-point function is .
In accordance with the central limit theorem, the density perturbations on the
scale of the spike are Gaussian for large and non-Gaussian for small .Comment: 15 pages in double column format, 6 figures. V2: Further
clarifications, updated to coincide with version published in Physics Letters
Boundary of the future of a surface
We prove that the boundary of the future of a surface K consists precisely of the points p that lie on a null geodesic orthogonal to K such that between K and p there are no points conjugate to K nor intersections with another such geodesic. Our theorem has applications to holographic screens and their associated light sheets and in particular enters the proof that holographic screens satisfy an area law