arXiv subjects

Etera Livine

Publications and source records attributed to Etera Livine.

7 recordsLinked to original sources

arXiv2026

Symmetries of cosmological perturbations: The residual low-multipole ambiguity

In cosmology, long-wavelength modes are related to large-gauge transformations (LGT), i.e. changes of coordinates that modify the physical geometry of the cosmological patch. These LGTs stand as bona-fide symmetries of cosmological perturbation theory with various applications, from consistency relations constraining cosmological correlators to non-linear conservation laws in the separate-universe approach. In this work, we revisit LGTs and derive two new results. First, we show that the global symmetries already identified in the literature can be extended to local infinite-dimensional symmetries. The associated generators depend on arbitrary functions of time, and generate low-multipole modes that modify the mean curvature energy and the angular momentum of the patch, demonstrating their physical nature. We propose to interpret these low-multipole soft modes as a new cosmological-frame ambiguity that needs to be fixed prior to evaluating cosmological observables. Second, we demonstrate that the adiabatic cosmological perturbations generated by LGTs deform but preserve all the explicit and hidden Killing symmetries of the background geometry. As such, long-wavelength modes stand as a concrete example of algebraically-special cosmological perturbations of Petrov-type O, and inherit the conformal group as isometries and a set of four deformed Killing-Yano tensors and their associated Killing tensors. This opens the possibility to study their effect on cosmological observables in a fully analytic manner.

gr-qc↗

arXiv2020

Twisted Geometries Coherent States for Loop Quantum Gravity

We introduce a new family of coherent states for loop quantum gravity, inspired by the twisted geometry parametrization. We compute their peakedness properties and compare them with the heat-kernel coherent states. They show similar features for the area and the holonomy operators, but improved peakedness in the direction of the flux. At the gauge-invariant level, the new family is built from tensor products of coherent intertwiners. To study the peakedness of the holonomy operator, we introduce a new shift operator based on the harmonic oscillator representation associated with the twisted geometry parametrization. The new shift operator captures the components of the holonomy relevant to disentangle its action into a simple positive shift of the spins.

gr-qc↗

arXiv2017

Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals

This is the first of a series of papers dedicated to the study of the partition function of three-dimensional quantum gravity on the twisted solid torus with the aim to deepen our understanding of holographic dualities from a non-perturbative quantum gravity perspective. Our aim is to compare the Ponzano-Regge model for non-perturbative three-dimensional quantum gravity with the previous perturbative calculations of this partition function. We begin by reviewing the results obtained in the past ten years via a wealth of different approaches, and then introduce the Ponzano--Regge model in a self-contained way. Thanks to the topological nature of three-dimensional quantum gravity we can solve exactly for the bulk degrees of freedom and identify dual boundary theories which depend on the choice of boundary states, that can also describe finite, non-asymptotic boundaries. This series of papers aims precisely at the investigation of the role played by the different quantum boundary conditions leading to different boundary theories. Here, we will describe the spin network boundary states for the Ponzano-Regge model on the twisted torus and derive the general expression for the corresponding partition functions. We identify a class of boundary states describing a tessellation with maximally fuzzy squares for which the partition function can be explicitly evaluated. In the limit case of a large, but finely discretized, boundary we find a dependence on the Dehn twist angle characteristic for the BMS3 character. We furthermore show how certain choices of boundary states lead to known statistical models as dual field theories-but with a twist.

hep-th↗

arXiv2017

Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters

We analyze the partition function of three-dimensional quantum gravity on the twisted solid tours and the ensuing dual field theory. The setting is that of a non-perturbative model of three dimensional quantum gravity--the Ponzano-Regge model, that we briefly review in a self-contained manner--which can be used to compute quasi-local amplitudes for its boundary states. In this second paper of the series, we choose a particular class of boundary spin-network states which impose Gibbons-Hawking-York boundary conditions to the partition function. The peculiarity of these states is to encode a two-dimensional quantum geometry peaked around a classical quadrangulation of the finite toroidal boundary. Thanks to the topological properties of three-dimensional gravity, the theory easily projects onto the boundary while crucially still keeping track of the topological properties of the bulk. This produces, at the non-perturbative level, a specific non-linear sigma-model on the boundary, akin to a Wess-Zumino-Novikov-Witten model, whose classical equations of motion can be used to reconstruct different bulk geometries: the expected classical one is accompanied by other "quantum" solutions. The classical regime of the sigma-model becomes reliable in the limit of large boundary spins, which coincides with the semiclassical limit of the boundary geometry. In a 1-loop approximation around the solutions to the classical equations of motion, we recover (with corrections due to the non-classical bulk geometries) results obtained in the past via perturbative quantum General Relativity and through the study of characters of the BMS3 group. The exposition is meant to be completely self-contained.

hep-th↗

arXiv2012

Exact and Approximate Unitary 2-Designs: Constructions and Applications

We develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming 2-designs have wide applicability to quantum information protocols. We devise an O(n)-size in-place circuit construction for an approximate unitary 2-design. We then show that this can be used to construct an efficient protocol for experimentally characterizing the fidelity of a quantum process on n qubits with quantum circuits of size O(n) without requiring any ancilla qubits, thereby improving upon previous approaches.

quant-ph↗

arXiv2007

LQG vertex with finite Immirzi parameter

We extend the definition of the "flipped" loop-quantum-gravity vertex to the case of a finite Immirzi parameter. We cover the Euclidean as well as the Lorentzian case. We show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity, and that the area operator has the same discrete spectrum as in loop quantum gravity. This includes the correct dependence on the Immirzi parameter, and, remarkably, holds in the Lorentzian case as well. The ad hoc flip of the symplectic structure that was initially required to derive the flipped vertex is not anymore needed for finite Immirzi parameter. These results establish a bridge between canonical loop quantum gravity and the spinfoam formalism in four dimensions.

gr-qc↗

arXiv2005

Convergence Conditions for Random Quantum Circuits

Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical framework for analyzing pseudo-random ensembles generated through a random circuit composition. We prove that the measure over random circuits converges exponentially (with increasing circuit length) to the uniform (Haar) measure on the unitary group and describe how the rate of convergence may be calculated for specific applications.

quant-ph↗