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Randomness is an essential tool in many disciplines of modern sciences, such as cryptography, black hole physics, random matrix theory, and Monte Carlo sampling. In quantum systems, random operations can be obtained via random circuits thanks to so-called q-designs and play a central role in condensed-matter physics and in the fast scrambling conjecture for black holes. Here, we consider a more physically motivated way of generating random evolutions by exploiting the many-body dynamics of a quantum system driven with stochastic external pulses. We combine techniques from quantum control, open quantum systems, and exactly solvable models (via the Bethe ansatz) to generate Haar-uniform random operations in driven many-body systems. We show that any fully controllable system converges to a unitary q-design in the long-time limit. Moreover, we study the convergence time of a driven spin chain by mapping its random evolution into a semigroup with an integrable Liouvillian and finding its gap. Remarkably, we find via Bethe-ansatz techniques that the gap is independent of q. We use mean-field techniques to argue that this property may be typical for other controllable systems, although we explicitly construct counterexamples via symmetry-breaking arguments to show that this is not always the case. Our findings open up new physical methods to transform classical randomness into quantum randomness, via a combination of quantum many-body dynamics and random driving.

Reference: L. Banchi, D. Burgarth, M. J. Kastoryano, Phys. Rev. X 7, 041015 (2017)

The surprising success of learning with deep neural networks poses two fundamental challenges: understanding why these networks work so well and what this success tells us about the nature of intelligence and our biological brain. Our recent Information Theory of Deep Learning shows that large deep networks achieve the optimal tradeoff between training size and accuracy, and that this optimality is achieved through the noise in the learning process.

In this talk, I will focus on the statistical physics aspects of our theory and the interaction between the stochastic dynamics of the training algorithm (Stochastic Gradient Descent) and the phase structure of the Information Bottleneck problem. Specifically, I will describe the connections between the phase transition and the final location and representation of the hidden layers, and the role of these phase transitions in determining the weights of the network.

Based partly on joint works with Ravid Shwartz-Ziv, Noga Zaslavsky, and Shlomi Agmon.

In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this talk, I will relax the assumption that quantum channels are combined classically, and I will show that, in certain situations, combining quantum channels in an indefinite causal order allows us to achieve tasks that are impossible in conventional quantum Shannon theory. Specifically, I will show a phenomenon of causal activation, whereby two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference.

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators.  We establish the existence of universal accumulation points in the spectrum at large s, s being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE and is analytic in s, analogous to the Caron-Huot formula for the four-point function. Some important assumptions are made in deriving this result: we comment on them.

In the last decades, advances in the level of precision in controlling atomic and optical systems opened up the low-energy precision frontier to fundamental physics tests. Exploitation of quantum entanglement in such systems to further improve the sensitivity of certain existing approaches is currently an active field of research. Drawing from the experiments in our lab, in this talk I will focus on the properties, generation and usage of a particular set of entangled states called spin squeezed states.

The lensing convergence measurable with future CMB experiments will be highly correlated with the clustering of galaxies that will be observed by imaging surveys such as LSST. I will discuss prospects for using that cross-correlation signal to constrain local primordial non-Gaussianity, the amplitude of matter fluctuations as a function of redshift, halo bias, and possibly the sum of neutrino masses. A key limitation for such analyses and large-scale structure analyses in general is that the mapping from initial conditions to observables is nonlinear for wavenumbers k>0.1h/Mpc. This can destroy cosmological information or move it to non-Gaussian tails of the probability distribution that are difficult to measure. I will describe how we can use recently developed initial condition reconstruction methods to help us recover some of that information in the nonlinear regime.