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A unidirectional optical oscillator is built by using a liquid crystal light-valve that couples a pump beam with the modes of a nearly spherical cavity. For sufficiently high pump intensity, the cavity field presents a complex spatio-temporal dynamics, accompanied by the emission of extreme waves and large deviations from the Gaussian statistics. We identify a mechanism of spatial symmetry breaking, due to a hypercycle-type amplification through the nonlocal coupling of the cavity field. . Associated with extreme waves are L-shaped statistics, with a probability of large peak occurrence much larger than predicted by Gaussian statistics. Different mechanisms to explain the origin of extreme waves have been proposed, including nonlinear focusing via modulational instability (MI) [4] and focusing of line currents [5]. In optical fibers, numerical simulations of the nonlinear Schrödinger equation (NLSE) [6] have established a direct analogy between optical and water rogue waves. In a spatially extended system, the formation of large amplitude and localized pulses, so-called optical needles, has been evidenced by numerical simulations for transparent media with saturating self-focusing nonlinearity [7]. Similar space-time phenomena, such as collapsing filaments, are also predicted in optical wave turbulence [8]. Recently, the spatio-temporal dynamics of MI-induced bright optical spots was observed in Ref. [9] and an algebraic power spectrum tail was reported due to momentum cascade [10]. Nevertheless, no experimental evidence has been given up to now of extreme waves in a spatially extended optical system.Here, we report, what is, at our knowledge, the first experimental evidence of extreme waves and non-Gaussian statistics in a 2D spatially extended optical system. The experiment consists of a nonlinear optical cavity, formed by a unidirectional ring oscillator with a liquid crystal light-valve (LCLV) as the gain medium. While for low pump the amplitude follows a Gaussian statistics, for sufficiently high pump we observe large deviations from Gaussianity, accompanied by the emission of extreme waves that appear on the transverse profile of the optical beam as genuine spatiotemporal phenomena, developing erratically in time and in space. The observations are confirmed by numerical simulation of the full model equations. Moreover, by introducing a mean-field simplified model, we show that extreme waves in the cavity are generated by a novel mechanism, which is based on a hypercycle-type amplification [11] occurring via nonlocal coupling of different spatial regions. The experimental setup is essentially the one described in [12]. The ring cavity is formed by three highreflectivity dielectric mirrors and a lens of f = 70 cm focal length. The total cavity length is L = 273.3 cm and the lens is positioned at a distance L 1 = 88.1 cm from the entrance plane of the LCLV. The coordinate system is taken such that z is along the cavity axis and x, y are on the transverse plane. A LCLV supplies the gain through a two-wave mixi...

In the presence of many waves, giant events can occur with a probability higher than expected for random dynamics. By studying linear light propagation in a glass fiber, we show that optical rogue waves originate from two key ingredients: granularity, or a minimal size of the light speckles at the fiber exit, and inhomogeneity, that is, speckles clustering into separate domains with different average intensities. These two features characterize also rogue waves in nonlinear systems; thus, nonlinearity just plays the role of bringing forth the two ingredients of granularity and inhomogeneity.

Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide the first proof that the number of continuous variables can not be smaller than 2N −2, N being the Hilbert space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods.

The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating a process of state preparation, transmission through the channel and subsequent measurement. It establishes a limit on the power of quantum communication in terms of classical resources. We show that classical simulations employing a finite amount of communication can be derived from a special class of hidden variable theories where quantum states represent statistical knowledge about the classical state and not an element of reality. This special class has attracted strong interest very recently. The communication cost of each derived simulation is given by the mutual information between the quantum state and the classical state of the parent hidden variable theory. Finally, we find that the communication complexity for single qubits is smaller than 1.28 bits. The previous known upper bound was 1.85 bits.