Talks

The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT) reduced to a spherical region. For example, when the excited state is a small perturbation of the vacuum state, the relative entropy is known to have a universal expression for all CFT’s. Specifically, the perturbative relative entropy can be written as the symplectic flux of a certain scalar field in an auxiliary AdS-Rindler spacetime. Moreover, if the CFT has a semi-classical holographic dual, the relative entropy is known to be related to conserved charges in the bulk dual spacetime. In this talk, I will introduce a one-parameter generalization of the relative entropy which I will call 'refined' Renyi relative entropy. I will use this quantity to present a one-parameter generalization of the aforementioned known results about the relative entropy. I will also discuss a new family of positive energy theorems in asymptotically locally AdS spacetimes that arises from the holographic dual of the refined Rényi relative entropy.

Quantum complexity is a notion characterizing the universality of the entanglement arising from a quantum evolution. A universal evolution will result in a complex entanglement. At the same time, this also corresponds to small fluctuations and to unlearnability from the point of view of machine learning. All these aspects are connected to the different features of k-designs, which are under-samplings of the Hilbert space. 

We study the transition in complexity due to the doping of a quantum circuit by universal gates and show that the transition to complex entanglement can be obtained by just a single gate. 
These results are relevant for the notions of scrambling, quantum chaos, OTOCs and operator spreading.

We conjecture that the transition to 4−design, W-D and unlearnability are one and the same.

What is the ultimate fate of black holes? Since the discovery of Hawking evaporation process, the issue has been much discussed. Loop quantum gravity suggests that black hole could ultimately turn into white holes. In this talk, we investigate several possible mixed scenario where black holes first evaporate to a Planckian size before tunnelling to white holes. We build various spacetime models, taking Hawking backreaction into account, and we discuss some aspects of the expected phenomenology. Finally, we will draw the path for a full LQG amplitude computation that could lead to observational predictions.

I will describe some connections between the Eigenstate Thermalization Hypothesis (ETH), the entanglement structure of generic excited eigenstates of chaotic quantum systems ("EE", arXiv:1906.04295), and the "bound on chaos" limiting the growth rate of the out-of-time-order four-point correlator in such systems ("OTOC", arXiv:1906.10808).

Higher spin symmetries are gauge symmetries sourced by massless particles with spin greater than two. When coupled with diffeomorphism, they give rise to higher spin gravity. After a review on higher spin gravity, I will discuss its holography and its embedding in the string theory. Finally I will talk about some applications of higher spin symmetry, both in string theory and in QFT. 

The discrete time-translation symmetry of a periodically-driven (Floquet) system allows for the existence of novel, nonequilibrium interacting phases of matter. A well-known example is the discrete time crystal, a phase characterized by the spontaneous breaking of this time-translation symmetry. In this talk, I will show that the presence of *multiple* time-translational symmetries, realized by quasiperiodically driving a system with two or more incommensurate frequencies, leads to a panoply of novel non-equilibrium phases of matter, both spontaneous symmetry breaking ("discrete time quasi-crystals") and topological. In order to stabilize such phases, I will outline rigorous mathematical results establishing slow heating of systems driven quasiperiodically at high frequencies. As a byproduct, I will introduce the notion of many-body localization (MBL) in quasiperiodically driven systems.