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One of the most peculiar features of quantum mechanics is the exponential growth of resources required to define the quantum state of a composite system. It makes it the direct simulation of even a handful of particles impossible in practice. This growth is due to the fact that the quantum state contains the full statistical information about the probabilities of any possible event. Since the quantum state is not a physically accessible observable, but can be statistically reconstructed only by performing many measurements on different replicas, it is natural to wonder if this resource excess is strictly necessary to describe the actual state of a single realization. The quantum probabilities could be reproduced by a theory where a single system carries less information than the quantum state. So, is the exponential complexity an intrinsic property of quantum systems or of the formalism? Is it possible to reduce the complexity in the single system representation by changing the formalism? These questions and their relation with quantum communication complexity are the main subject of my research.

- 2005-present High school teacher, Italy (on leave).
- 2001-2009 post-doctoral fellow and research contract at Universita' di Firenze, Italy

- A. Montina, "Epistemic view of quantum states and communication complexity of quantum channels", Phys. Rev. Lett. 109, 110501 (2012). Marked as "Editors' suggestion".
- S. Residori, U. Bortolozzo, A. Montina, F. Lenzini, F. T. Arecchi, "Rogue waves in spatially extended optical systems", Fluctuation and Noise Letters 11, 1240014 (2012)
- A. Montina, "Dynamics of a qubit as a classical stochastic process with time-correlated noise: Minimal measurement invasiveness", Phys. Rev. Lett. 108, 160501 (2012). arXiv: 1108.5138
- A. Montina, "Communication cost of classically simulating a quantum channel with subsequent rank-1 projective measurement", Phys. Rev. A 84 (Rapid Communication), 060303(R) (2011), arXiv: 1110.5944
- Alberto Montina, Approximate simulation of entanglement with a linear cost of communication, Phys. Rev. A 84, 042307 (2011), arXiv: 1107.4647
- F. T. Arecchi, U. Bortolozzo, A. Montina, S. Residori, "Granularity and Inhomogeneity Are the Joint Generators of Optical Rogue Waves", Phys. Rev. Lett. 106, 153901 (2011).
- Z. Chen, A. Montina, "Measurement contextuality is implied by macroscopic realism", Phys. Rev. A 83, 042110 (2011), arXiv: 1012.2122
- A. Montina, "State-space dimensionality in short-memory hidden-variable theories", Phys. Rev. A 83, 032107 (2011), arXiv: 1008.4415
- A. Montina, "Compressing the hidden variable space of a qubit", Phys. Lett. A 375, 1385 (2011)
- A. Montina, U. Bortolozzo, S. Residori, and F. T. Arecchi, "Non-Gaussian Statistics and Extreme Waves in a Nonlinear Optical Cavity", Phys. Rev. Lett. 103, 173901 (2009)
- M. Ciszak, A. Montina, F. T. Arecchi, "Control of transient synchronization with external stimuli", Chaos 19, 015104 (2009)
- M. Ciszak, A. Montina, F. T. Arecchi, "Spike synchronization of chaotic oscillators as a phase transition", Cognitive Processing 10, S33 (2009)
- M. Ciszak, A. Montina, F. T. Arecchi, " Sharp versus smooth synchronization transition of locally coupled oscillators", Phys. Rev. E 78, 016202 (2008)
- A. Montina, F. T. Arecchi, "Quantum decoherence reduction by increasing the thermal bath temperature", Phys. Rev. Lett. 100, 120401 (2008)
- A. Montina, "Exponential complexity and ontological theories of quantum mechanics", Phys. Rev. A 77, 022104 (2008)
- S. Residori, U. Bortolozzo, A. Montina, F. T. Arecchi, J. P. Huignard, "A novel type of optical oscillator based on a liquid crystal gain medium", Journal of nonlinear optical physics & materials 16, 343 (2007)
- U. Bortolozzo, A. Montina, F. T. Arecchi, J. P. Huignard, S. Residori, "Spatiotemporal pulses in a liquid crystal optical oscillator", Phys. Rev. Lett. 99, 023901 (2007).
- A. Montina, C. Mendoza, F. T. Arecchi, "Role of refractory period in homoclinic models of neural synchronization",International Journal of Neural Systems 17, 79 (2007)
- A. Montina, U. Bortolozzo, S. Residori, J. P. Huignard, F. T. Arecchi, "Complex dynamics of a unidirectional optical oscillator based on a liquid-crystal gain medium", Phys. Rev. A 76, 033826 (2007)
- A. Montina, "Statistical representation of quantum states", J. Phys.: Conf. Ser. 67, 012050 (2007)
- A. Montina, "Condition for any realistic theory of quantum systems", Phys. Rev. Lett. 97, 180401 (2006)
- A. Montina, "Exact BCS stochastic schemes for a time-dependent many-body fermionic system", Phys. Rev. A 73, 013618 (2006)
- A. Montina, F. T. Arecchi, "Dynamics of narrow bright solitons in an array of attractive atoms in a Bose-Einstein condensate", Phys. Rev. Lett. 94 230402 (2005)
- A. Montina, F. T. Arecchi, "Many-body ground-state properties of an attractive Bose-Einstein condensate in a one-dimensional ring", Phys. Rev. A 71 063615 (2005)
- F. T. Arecchi, A. Montina, "Macroscopic quantum coherence in Bose-Einstein condensates", Quantum Computers and Computing 5, 42 (2005)
- A. Montina, F. T. Arecchi, "Atomic density fluctuations in Bose-Einstein condensates", Phys. Rev. A 68, 053608 (2003)
- A. Montina, "Gauge-P representation and N-boson problem with binary interactions", Phys. Rev. A 68, 043616 (2003)
- A. Montina, "Thermalization of an impurity cloud in a Bose-Einstein condensate", Phys. Rev. A 67, 053614 (2003)
- A. Montina, "First-order coherence in an atomic condensate at finite temperature", Phys. Rev. A 67, 043604 (2003)
- A. Montina, F. T. Arecchi, "Macroscopic quantum coherence in a repulsive Bose-Einstein condensate", Phys. Rev. A 67, 023616 (2003)
- A. Montina, "Impurity scattering in a Bose-Einstein condensate at finite temperature", Phys. Rev. A 66, 023609 (2002)
- A. Montina, "Bistability and macroscopic quantum coherence in a Bose-Einstein condensate of Lithium-7", Phys. Rev. A 66, 013605 (2002)
- A. Montina, F. T. Arecchi, "Bistability and macroscopic quantum coherence in BECs: the two cases of attractive and repulsive interactions", Journal of Modern Optics 49, 319 (2002)
- A. Montina, E. Arimondo, "Correlation functions for a Bose-Einstein condensate in the Bogoliubov approximation", European Physical Journal D 14, 105 (2001)
- F. T. Arecchi, A. Montina, "Quantum interference between macroscopically distinct optical states", Fortschritte der Physik-Progress of Physics 48, 423 (2000)
- A. Montina, R. Mannella, E. Arimondo, "Excitation frequencies and stability regions for two-species Bose-Einstein condensate in a triaxial magnetic trap", Phys. Lett. A 261, 337 (1999)
- A. Montina, F. T. Arecchi, "Toward an optical evidence of quantum interference between macroscopically distinct states", Phys. Rev. A 58, 3472 (1998)
- Output-sensitive algorithm for generating the flats of a matroid, A. Montina, arXiv: 1107.4301
- Dynamical systems and irreversibility: proceedings of the XXI Solvay Conference On Physics

- "Ontological dimension and quantum information complexity", Workshop: 'Quantum States: ontic or epistemic?', University of Aberdeen
- "Statistical representation of quantum states", Conference: New Frontiers in Quantum Foundations, CUPI 2011, Clemson Univ.
- "Resource cost in the classical simulation of a quantum preparation-measurement process", Conference: 21st-Century directions in de Broglie-Bohm theory and beyond, Tuscany
- PIRSA:11050025, How many classical resources are required for representing a quantum system?, 2011-05-31, Quantum Foundations
- PIRSA:09090085, Does the wave-function concern information or reality? Further progress towards an answer, 2009-09-28, PIAF 09' New Perspectives on the Quantum State
- PIRSA:08120038, Does the wave-function concern information or reality, 2008-12-12, Young Researchers Conference 2008

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