6 research outputs found
On the fate of the Hoop Conjecture in quantum gravity
We consider a closed region of 3d quantum space modeled by
spin-networks. Using the concentration of measure phenomenon we prove that,
whenever the ratio between the boundary and the bulk edges of the
graph overcomes a finite threshold, the state of the boundary is always
thermal, with an entropy proportional to its area. The emergence of a thermal
state of the boundary can be traced back to a large amount of entanglement
between boundary and bulk degrees of freedom. Using the dual geometric
interpretation provided by loop quantum gravity, we interprete such phenomenon
as a pre-geometric analogue of Thorne's "Hoop conjecture", at the core of the
formation of a horizon in General Relativity.Comment: 7 pages, 2 figures, minor improvement
Typicality in spin network states of quantum geometry
In this work, we extend the so-called typicality approach, originally
formulated in statistical mechanics contexts, to -invariant spin-network
states. Our results do not depend on the physical interpretation of the spin
network; however, they are mainly motivated by the fact that spin-network
states can describe states of quantum geometry, providing a gauge-invariant
basis for the kinematical Hilbert space of several background-independent
approaches to quantum gravity. The first result is, by itself, the existence of
a regime in which we show the emergence of a typical state. We interpret this
as the proof that in that regime there are certain (local) properties of
quantum geometry which are "universal". Such a set of properties is heralded by
the typical state, of which we give the explicit form. This is our second
result. In the end, we study some interesting properties of the typical state,
proving that the area law for the entropy of a surface must be satisfied at the
local level, up to logarithmic corrections which we are able to bound.Comment: Typos and mistakes fixe
Quantifying the difference between many-body quantum states
The quantum state overlap is the textbook measure of the difference between
two quantum states. Yet, it is inadequate to compare the complex configurations
of many-body systems. The problem is inherited by the widely employed quantum
state fidelity and related distances. We introduce the weighted distances, a
new class of information-theoretic measures that overcome these limitations.
They quantify how hard it is to discriminate between two quantum states of many
particles, factoring in the structure of the required measurement apparatus.
Therefore, they can be used to evaluate both the theoretical and the
experimental performances of complex quantum devices. We also show that the
newly defined "weighted Bures length" between the input and output states of a
quantum process is a lower bound to the experimental cost of the
transformation. The result uncovers an exact quantum limit to our ability to
convert physical resources into computational ones.Comment: 4+2 pages, change from previous version: the contractivity of
weighted distances holds only for single site operation
A note on the secondary simplicity constraints in loop quantum gravity
15 pagesInternational audienceA debate has appeared in the literature on loop quantum gravity and spin foams, over whether secondary simplicity constraints should imply the shape matching conditions reducing twisted geometries to Regge geometries. We address the question using a model in which secondary simplicity constraints arise from a dynamical preservation of the primary ones, and answer it in the affirmative. The origin of the extra condition is to be found in the different graph localisations of the various constraints. Our results are consistent with previous claims by Dittrich and Ryan, and extend their validity to Lorentzian signature and a priori arbitrary cellular decompositions. Finally, we show how the (gauge-invariant version of the) twist angle {\xi} featuring in twisted geometries equals on-shell the Regge dihedral angle multiplied by the Immirzi parameter, thus recovering the discrete extrinsic geometry from the Ashtekar-Barbero holonomy