**En el AULA SEMINARIO, 2do piso, Pab. I,**

**1- Lunes 3/12 – 14hs
RAJARSHI ROY (University of Maryland)**

**Random Numbers from Light: Photons, Time delays, Chaos and Entropy**

**2- Martes 4/12 – 11hs
YELENA GURYANOVA (IQOQI Vienna)**

**Ideal Projective Measurements Have Infinite Resource Costs**

**3- Martes 4/12 – 14hs
ALBERT DIAZ-GUILERA (Universitat de Barcelona)**

**Nonlinear dynamics in multiplex networks**

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** Rajarshi Roy
University of Maryland**

**Random Numbers from Light: Photons, Time delays, Chaos and Entropy**

Many physical processes, including the intensity fluctuations of a chaotic laser, the detection of single photons, and the Brownian motion of a microscopic particle in a fluid are unpredictable, at least on long timescales. This unpredictability can be due to a variety of physical mechanisms, but it is quantified by an entropy rate. This rate, which describes how quickly a system produces new and random information, is fundamentally important in statistical mechanics and practically important for random number generation. We experimentally study entropy generation and the emergence of deterministic chaotic dynamics from discrete noise in a system that applies feedback to a weak optical signal at the single-photon level. We show that in this system the dynamics transition from shot noise to chaos as the photon rate increases and that the entropy rate can reflect either the deterministic or noisy aspects of the system depending on the sampling rate and resolution of the measurements.

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**Yelena Guryanova
IQOQI Vienna**

**Ideal Projective Measurements Have Infinite Resource Costs**

We show that it is impossible to perform ideal projective measurements on quantum systems using finite resources. We identify three fundamental features of an ideal projective measurement and show that when limited by finite resources only one of these features can be salvaged. Using an explicit model of an N-particle detector perfectly reproducing the statistics of the system, we provide tight analytic expressions for the energy cost of performing a measurement. This cost may be broken down into two parts. First, the cost of preparing the pointer in a suitable state, and second, the cost of a global interaction between the system and pointer in order to correlate them. Our results show that, even under the assumption that the interaction can be controlled perfectly, achieving perfect correlation is infinitely expensive. We provide protocols for achieving optimal correlation given finite resources.

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**Albert Diaz-Guilera
Universitat de Barcelona.**

**Nonlinear dynamics in multiplex networks**

We will show some of the recent result in our group concerning dynamics in multiplex networks. On the one hand we consider multiplex networks as set of nodes in different layers. At each layer the set of nodes is the same but the connections among the nodes can be different in the layers.Furthermore the connections among the layers is described by a ”network of layers”. We have studied different processes across the layers (diffusion) and between the layers (reaction) [1]. In this case Turing patterns appear as an effect of different average connectivities in different layers [2].

We also show that a multiplex construction where the layers correspond to contexts in which agents make different sets of connections can make a model of opinion formation to show stationary states of coexistence that are not observed in simple layers [3]. Finally, as a particular case of multiplex network, one can also analyze networks that change in time, since in this case each layer of the multiplex corresponds to a snapshot of the interaction pattern. For this situation, we have shown that there are different mechanisms that dominate the diffusion of information in the system depending on the relative effect of mobility and diffusion among the nodes

[1] Replicator dynamics with diffusion on multiplex networks. RJ Requejo, A. Diaz-Guilera. Physical Review E 94, 022301 (2016)

[2] Pattern formation in multiplex networks. NE Kouvaris, S Hata, A. Diaz-Guilera. Scientific Reports 5, Article number: 10840 (2015)

[3] Opinion competition dynamics on multiplex networks. R Amato, N E Kouvaris, M San Miguel and Albert Diaz-Guilera. New J Phys 19, 123019 (2017).

[4] Tuning Synchronization of Integrate-and-Fire Oscillators through Mobility. L. Prignano, O. Sagarra, and A. DAaz-Guilera ̃Phys. Rev. Lett. 110, 114101 (2013)

[5] Synchronization in dynamical networks of locally coupled self-propelled oscillators. D. Levis, I. Pagonabarraga,