Measures and applications of quantum correlations, Journal of Physics A: Mathematical and Theoretical, vol.49, issue.47, p.473001, 2016. ,
DOI : 10.1088/1751-8113/49/47/473001
Entanglement Spectrum of the Two-Dimensional Bose-Hubbard Model, Physical Review Letters, vol.110, issue.26, 2013. ,
DOI : 10.1007/978-3-642-10589-0
Oscillating Superfluidity of Bosons in Optical Lattices, Physical Review Letters, vol.317, issue.25, 2002. ,
DOI : 10.1103/PhysRevB.59.14054
Phase diagram of two-component bosons on an optical lattice, New Journal of Physics, vol.5, p.113, 2003. ,
DOI : 10.1088/1367-2630/5/1/113
Entanglement in many-body systems, Reviews of Modern Physics, vol.43, issue.2, 2008. ,
DOI : 10.1103/RevModPhys.75.715
Considerations on the Flow of Superfluid Helium, Reviews of Modern Physics, vol.78, issue.2, pp.298-310, 1966. ,
DOI : 10.1103/PhysRev.78.818
Entropy inequalities, pp.160-170, 1970. ,
DOI : 10.1007/978-3-642-55925-9_4
Atomic Coherent States in Quantum Optics, Physical Review A, vol.3, issue.6, pp.2211-2237, 1972. ,
DOI : 10.1007/BF01645412
: A New Violation of Bell's Inequalities, Physical Review Letters, vol.14, issue.2, pp.91-94, 1982. ,
DOI : 10.1103/PhysRevD.14.1944
Fluctuations of the number of particles within a given volume in cold quantum gases, Physical Review A, vol.76, issue.6, 2007. ,
DOI : 10.1103/PhysRevLett.93.200404
Local hiddenvariable models for entangled quantum states, Journal of Physics A: Mathematical and Theoretical, vol.4742, p.424002, 2014. ,
A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice, Nature, vol.79, issue.7269, p.74, 2009. ,
DOI : 10.1103/PhysRevA.80.021602
Black Holes and Entropy, Physical Review D, vol.161, issue.8, pp.2333-2346, 1973. ,
DOI : 10.1086/150515
On the Einstein Podolski Rosen paradox, In: Physics, vol.1, issue.3, pp.195-200, 1964. ,
Geometry of Quantum States: An Introduction to Quantum Entanglement, p.9781139453462, 2007. ,
Mutual information area laws for thermal free fermions, Journal of Statistical Mechanics: Theory and Experiment 2015.2, P02008. URL: http : / / stacks . iop . org, pp.1742-5468, 2015. ,
DOI : 10.1088/1742-5468/2015/02/P02008
On the duality condition for quantum fields, Journal of Mathematical Physics, vol.17, issue.3, pp.303-321, 1976. ,
DOI : 10.1063/1.522898
Interferometric visibility and coherence, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, vol.116, issue.2203, 2017. ,
DOI : 10.1103/PhysRevLett.116.160406
Quantum Theory of Finite Systems, pp.9780262022149-117, 1986. ,
Many-body physics with ultracold gases, Reviews of Modern Physics, vol.91, issue.196, pp.885-964, 2008. ,
DOI : 10.1103/PhysRevLett.91.250401
URL : https://hal.archives-ouvertes.fr/hal-00195515
A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II, Physical Review, vol.61, issue.2, pp.166-193, 1952. ,
DOI : 10.1103/PhysRev.47.777
Quantum spin dynamics and entanglement generation with hundreds of trapped ions, Science 352.6291, pp.1297-1301, 2016. ,
DOI : 10.1103/PhysRevLett.109.020503
The Quantum Postulate and the recent Development of Atomic Theory, Nature, vol.121, 1928. ,
Spin- and density-resolved microscopy of antiferromagnetic correlations in Fermi-Hubbard chains, Science 353.6305, pp.1257-1260, 2016. ,
DOI : 10.1103/PhysRevB.43.3706
Optimal frequency measurements with maximally correlated states, Physical Review A, vol.10, issue.6, pp.4649-4652, 1996. ,
DOI : 10.1109/TIM.1990.1032897
URL : http://www.boulder.nist.gov/timefreq/general/pdf/1181.pdf
Zur Quantenmechanik der Stossvorgänge English translation in Quantum Theory and Measurement, Zeitschrift für Physik 37, pp.863-67, 1926. ,
Size Scaling for Infinitely Coordinated Systems, Physical Review Letters, vol.43, issue.7, pp.478-481, 1982. ,
DOI : 10.1103/PhysRevLett.43.744
Bell nonlocality, Reviews of Modern Physics, vol.1, issue.8, pp.419-478, 2014. ,
DOI : 10.1103/PhysRevLett.71.4287
Entanglement entropy and quantum field theory Journal of Statistical Mechanics: Theory and Experiment, p.171, 2004. ,
Exact relations between particle fluctuations and entanglement in Fermi gases, EPL (Europhysics Letters) 98.2, p.67, 2012. ,
DOI : 10.1209/0295-5075/98/20003
Irreversibility and Generalized Noise, Physical Review, vol.19, issue.1, pp.34-40, 1951. ,
DOI : 10.1007/BF01327565
Entanglement entropy in free quantum field theory, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.50, 2009. ,
DOI : 10.1088/1751-8113/42/50/504007
Quantum steering: a review with focus on semidefinite programming, Reports on Progress in Physics, vol.80, issue.2, p.24001, 2017. ,
DOI : 10.1088/1361-6633/80/2/024001
How Universal Is the Entanglement Spectrum?, Physical Review Letters, vol.113, issue.6, 2014. ,
DOI : 10.1103/PhysRevB.89.115116
Entanglement contour, Journal of Statistical Mechanics: Theory and Experiment 10, pp.80-82, 2014. ,
DOI : 10.1088/1742-5468/2014/10/P10011
Semiclassical approach to ground-state properties of hard-core bosons in two dimensions, Physical Review B, vol.85, issue.10, 2012. ,
DOI : 10.1103/PhysRevA.8.1111
URL : https://hal.archives-ouvertes.fr/hal-00703456
Magnetic Critical Scattering Oxford Series on Neutron Scattering in Condensed Matter, pp.37-39, 0194. ,
A contour for the entanglement entropies in harmonic lattices, Journal of Physics A: Mathematical and Theoretical, vol.50, issue.31, 2017. ,
DOI : 10.1088/1751-8121/aa7902
Infinite-range Ising ferromagnet in a time-dependent transverse magnetic field: Quench and ac dynamics near the quantum critical point, Physical Review B, vol.67, issue.14, 2006. ,
DOI : 10.1103/PhysRevA.70.062304
Reflection of Electrons by a Crystal of Nickel, Proceedings of the National Academy of Sciences of the United States of America 14, pp.317-322, 1928. ,
DOI : 10.1073/pnas.14.4.317
Ultracold atoms in optical lattices, Physical Review A, vol.46, issue.4, 2003. ,
DOI : 10.1103/PhysRevB.46.9051
Entanglement entropy and mutual information in Bose-Einstein condensates, Physical Review A, vol.2, issue.1, 2009. ,
DOI : 10.1103/PhysRev.83.678
Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model, Physical Review Letters, vol.3, issue.23, p.210, 2004. ,
DOI : 10.1103/PhysRev.93.99
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, Physical Review, vol.47, issue.10, pp.777-780, 1935. ,
DOI : 10.1103/PhysRev.47.777
¨ Uber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt English translation in " The Old Quantum Theory, Annalen der Physik D. ter Haar, vol.17, pp.132-148, 1905. ,
: Area laws for the entanglement entropy, Reviews of Modern Physics, vol.2, issue.1, pp.277-306, 2010. ,
DOI : 10.1103/PhysRevA.58.883
Analytical results for the entanglement Hamiltonian of a free-fermion chain, Journal of Physics A: Mathematical and Theoretical, vol.50, issue.28, 2017. ,
DOI : 10.1088/1751-8121/aa76b5
The ???Higgs??? amplitude mode at the two-dimensional superfluid/Mott insulator transition, Nature, vol.487, issue.7408, pp.454-458, 2012. ,
DOI : 10.1103/PhysRevLett.83.4690
URL : https://hal.archives-ouvertes.fr/hal-01397828
Quantum mechanics and path integrals. International series in pure and applied physics, 1965. ,
Boson localization and the superfluid-insulator transition, Physical Review B, vol.61, issue.1, pp.546-570, 1989. ,
DOI : 10.1103/PhysRevLett.61.1950
Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions Advanced book classics, pp.9780201410495-29, 1995. ,
Entanglement and fluctuations in the XXZ model with power-law interactions, Physical Review B, vol.95, issue.24, 2017. ,
DOI : 10.1103/PhysRevB.93.205120
Area law and its violation: A microscopic inspection into the structure of entanglement and fluctuations, Physical Review B, vol.92, issue.11, pp.80-82, 2015. ,
DOI : 10.1103/PhysRevB.88.144426
Slave Boson Formulation for Interacting Boson Systems and the Superfluid-Insulator Transition " . In: eprint arXiv:cond-mat/9405053, p.9405053, 1994. ,
Inequalities for quantum Fisher information, Proc. Amer. Math. Soc. 137, pp.317-344, 2009. ,
DOI : 10.1090/S0002-9939-08-09447-1
Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture, Physical Review Letters, vol.285, issue.10, p.100503, 2006. ,
DOI : 10.1007/BF02183366
Significant-Loophole-Free Test of Bell???s Theorem with Entangled Photons, Physical Review Letters, vol.1, issue.25, 2015. ,
DOI : 10.1103/PhysRevLett.112.110405
Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature, vol.4156867, issue.105, pp.39-44, 2002. ,
Metric adjusted skew information, Proceedings of the National Academy of Sciences 105.29, pp.9909-9916, 2008. ,
DOI : 10.1109/TIT.2005.858971
URL : http://www.pnas.org/content/105/29/9909.full.pdf
Measuring Renyi Entanglement Entropy in Quantum Monte??Carlo Simulations, Physical Review Letters, vol.104, issue.15, p.157201, 2010. ,
DOI : 10.1103/PhysRevLett.99.167204
Measuring multipartite entanglement through dynamic susceptibilities, Nature Physics, vol.5, issue.8, pp.778-782, 2016. ,
DOI : 10.1103/PhysRevB.56.11659
Black hole explosions?, Nature, vol.7, issue.5443, pp.30-31, 1974. ,
DOI : 10.1093/mnras/152.1.75
English translation in Quantum Theory and Measurement, Zeitschrift für Physik 43 ,
Entanglement entropy scaling in the bilayer Heisenberg spin system, Physical Review B, vol.89, issue.24, 2014. ,
DOI : 10.1103/PhysRevB.83.174416
Classical, quantum and total correlations, Journal of Physics A: Mathematical and General, vol.34, issue.35, pp.6899-6905, 2001. ,
DOI : 10.1088/0305-4470/34/35/315
Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres, Nature, vol.484, issue.7575, pp.682-686, 2015. ,
DOI : 10.1038/nature11023
Entanglement area law in superfluid 4 He, 2016. ,
Theory of dynamic critical phenomena, Reviews of Modern Physics, vol.30, issue.88, pp.435-479, 1977. ,
DOI : 10.1103/PhysRevLett.30.22
Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet, Physical Review, vol.57, issue.12, pp.1098-1113, 1940. ,
DOI : 10.1103/PhysRev.57.142
Information-theoretic aspects of inseparability of mixed states, Physical Review A, vol.210, issue.3, pp.1838-1843, 1996. ,
DOI : 10.1016/S0375-9601(96)80001-6
Quantum entanglement, Reviews of Modern Physics, vol.93, issue.2, pp.865-942, 2009. ,
DOI : 10.1103/PhysRevA.58.883
Dynamical properties of ultracold bosons in an optical lattice, Physical Review B, vol.6, issue.8, 2007. ,
DOI : 10.1103/PhysRevB.32.1464
Composite Boson Mapping for Lattice Boson Systems, Physical Review Letters, vol.111, issue.4, p.45701, 2013. ,
DOI : 10.1103/PhysRevLett.109.010401
Quantum Monte Carlo calculation of entanglement R??nyi entropies for generic quantum systems, Physical Review B, vol.86, issue.23, 2012. ,
DOI : 10.1088/1751-8113/42/50/504007
Fisher information and multiparticle entanglement, Physical Review A, vol.7, issue.2, p.220, 2012. ,
DOI : 10.1103/PhysRevA.85.022322
URL : http://arxiv.org/pdf/1006.4366
Onset of a quantum phase transition with a trapped ion quantum simulator, Nature Communications, vol.43, issue.2, p.377, 2011. ,
DOI : 10.1103/PhysRevLett.105.090502
Measuring entanglement entropy in a quantum manybody system " . In: Nature 528, pp.77-83, 2015. ,
The Conceptual Development of Quantum Mechanics. International series in pure and applied physics, 1966. ,
Anomalies in the entanglement properties of the squarelattice Heisenberg model, Phys. Rev. B, vol.84, issue.137, 2011. ,
Field Theory of Non-Equilibrium Systems, pp.37-39, 2011. ,
DOI : 10.1017/CBO9781139003667
Statistical Physics of Fields, p.9780521873413, 2007. ,
DOI : 10.1017/CBO9780511815881
Quantum simulation of the transverse Ising model with trapped ions, New Journal of Physics, vol.13, issue.10, p.105003, 2011. ,
DOI : 10.1088/1367-2630/13/10/105003
Evolution of Quantum Fluctuations Near the Quantum Critical Point of the Transverse Field Ising Chain System CoNb 2 O 6, Phys. Rev. X, vol.4, issue.3, 2014. ,
Local atom-number fluctuations in quantum gases at finite temperature, Physical Review A, vol.84, issue.3, 2011. ,
DOI : 10.1098/rsta.1955.0005
Criticality in correlated quantum matter, Nature Physics, vol.400, issue.1, pp.53-56, 2005. ,
DOI : 10.1016/0550-3213(93)90414-K
Quantum entanglement in condensed matter systems, Physics Reports, vol.646, issue.68, pp.1-59, 2016. ,
DOI : 10.1016/j.physrep.2016.06.008
URL : https://hal.archives-ouvertes.fr/hal-01384552
Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids, Journal of Statistical Mechanics: Theory and Experiment, vol.2014, issue.11, 2014. ,
DOI : 10.1088/1742-5468/2014/11/P11013
URL : https://hal.archives-ouvertes.fr/hal-01126637
Creation of a six-atom, Nature, vol.4387068, pp.639-642, 2005. ,
Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems, OUP Oxford. ISBN, p.9780191627439, 2012. ,
DOI : 10.1093/acprof:oso/9780199573127.001.0001
Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States, Physical Review Letters, vol.101, issue.1, p.10504, 2008. ,
DOI : 10.1103/PhysRevLett.100.246802
Proof of the strong subadditivity of quantummechanical entropy, Journal of Mathematical Physics, vol.1412, pp.1938-1941, 1973. ,
Two soluble models of an antiferromagnetic chain, Annals of Physics, vol.163, issue.61, pp.407-466, 1961. ,
Universal logarithmic corrections to entanglement entropies in two dimensions with spontaneously broken continuous symmetries, Physical Review B, vol.91, issue.15, 2015. ,
DOI : 10.1088/1742-5468/2011/05/P05001
URL : https://hal.archives-ouvertes.fr/hal-01153291
Thermodynamics of strongly interacting bosons on a lattice : new insights and numerical approaches URL: https : / / tel . archives -ouvertes, pp.1451352-228, 2016. ,
Quantum Correlations, Separability, and Quantum Coherence Length in Equilibrium Many-Body Systems, Physical Review Letters, vol.117, issue.13, 2016. ,
DOI : 10.1017/CBO9780511973765
Extending Noether???s theorem by quantifying the asymmetry of quantum states, Nature Communications, vol.40, issue.3821, 2014. ,
DOI : 10.1063/1.532887
Entanglement Entropy of Systems with Spontaneously Broken Continuous Symmetry, p.169, 2011. ,
Entanglement entropy in the O(N ) model, Phys. Rev. B, vol.80, issue.170, p.171, 2009. ,
The classical-quantum boundary for correlations: Discord and related measures, Reviews of Modern Physics, vol.9, issue.4, pp.1655-1707, 2012. ,
DOI : 10.1103/PhysRevA.81.062110
14-Qubit Entanglement: Creation and Coherence, Physical Review Letters, vol.106, issue.13, 2011. ,
DOI : 10.1088/1367-2630/12/9/095019
URL : http://arxiv.org/pdf/1009.6126
Quantum Computation and Quantum Information, p.61, 2000. ,
Theory Of Quantum Liquids Advanced Books Classics, p.9780813346533, 1999. ,
Quantum Discord: A Measure of the Quantumness of Correlations, Physical Review Letters, vol.89, issue.1, 2001. ,
DOI : 10.1103/RevModPhys.50.221
Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model, Science 353.6305, pp.1253-1256, 2016. ,
DOI : 10.7717/peerj.453
Signatures of the superfluid to Mott insulator transition in equilibrium and in dynamical ramps, Physical Review B, vol.86, issue.14, 2012. ,
DOI : 10.1103/PhysRevB.86.054508
Bose-Einstein Condensation and Liquid Helium, Physical Review, vol.93, issue.3, pp.576-584, 1956. ,
DOI : 10.1103/PhysRev.93.1412.2
Reduced density matrices and entanglement entropy in free lattice models, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.50, pp.504003-79, 2009. ,
DOI : 10.1088/1751-8113/42/50/504003
Monotone metrics on matrix spaces, Linear Algebra and its Applications, vol.244, issue.277, pp.81-96, 1996. ,
DOI : 10.1016/0024-3795(94)00211-8
URL : https://doi.org/10.1016/0024-3795(94)00211-8
Quantum theory of phase estimation Enrico Fermi URL: https, Proceedings of the International School of Physics, pp.691-718, 2014. ,
Non-classical states of atomic ensembles: fundamentals and applications in quantum metrology, pp.204-210, 2016. ,
Entanglement, Nonlinear Dynamics, and the Heisenberg Limit, Physical Review Letters, vol.304, issue.10, 2009. ,
DOI : 10.1103/PhysRevLett.99.223602
The one-dimensional Ising model with a transverse field, Annals of Physics, vol.57, issue.1, 1970. ,
DOI : 10.1016/0003-4916(70)90270-8
Generalized Geometric Quantum Speed Limits, Physical Review X, vol.9, issue.2, 2016. ,
DOI : 10.1080/09500349414552171
URL : http://doi.org/10.1103/physrevx.6.021031
Bose-Einstein Condensation. International Series of Monographs on Physics, pp.9780198507192-110, 2003. ,
Quantum gas microscopy with spin, atom-number, and multilayer readout, Physical Review A, vol.91, issue.4, 2015. ,
DOI : 10.1103/PhysRevA.86.033618
URL : http://arxiv.org/pdf/1504.05250
Atomic Bose-Hubbard systems with single -particle atomic control, 2015. ,
Quantum Phase Transitions ISBN: 9780521004541 (cit, 2001. ,
Universal quantum-critical dynamics of two-dimensional antiferromagnets, Physical Review Letters, vol.42, issue.16, pp.2411-2414, 1992. ,
DOI : 10.1103/PhysRevB.42.2485
An Undulatory Theory of the Mechanics of Atoms and Molecules, Physical Review, vol.38, issue.6, pp.1049-70, 1926. ,
DOI : 10.1007/BF01399113
Die gegenw???rtige Situation in der Quantenmechanik, Die Naturwissenschaften, vol.23, issue.48, pp.807-812, 1935. ,
DOI : 10.1007/BF01491891
Mott-insulator???to???superfluid transition in the Bose-Hubbard model: A strong-coupling approach, Physical Review A, vol.617, issue.3, 2005. ,
DOI : 10.1103/PhysRevA.68.043623
URL : https://hal.archives-ouvertes.fr/hal-00117529
Strong Loophole-Free Test of Local Realism, Phys. Rev. Lett, vol.11525, 2015. ,
Thermodynamic singularities in the entanglement entropy at a two-dimensional quantum critical point, Physical Review B, vol.9, issue.7, 2012. ,
DOI : 10.1126/science.1212207
Entanglement entropy of the two-dimensional Heisenberg antiferromagnet, Physical Review B, vol.83, issue.22, pp.139-169, 2011. ,
DOI : 10.1103/PhysRevLett.73.886
Bipartite fluctuations as a probe of many-body entanglement, Physical Review B, vol.58, issue.3, p.61, 2012. ,
DOI : 10.1073/pnas.0703293104
URL : https://hal.archives-ouvertes.fr/hal-00703455
Entanglement and Extreme Spin Squeezing, Physical Review Letters, vol.404, issue.20, pp.4431-4434, 2001. ,
DOI : 10.1038/35005011
Quantum Coherence as a Resource, p.50, 2016. ,
An Introduction to Black Holes, Information and the String Theory Revolution: The Holographic Universe, World Scientific, pp.71-74, 2005. ,
DOI : 10.1142/5689
Structure of entanglement in regulated Lorentz invariant field theories, 2013. ,
Area law for gapless states from local entanglement thermodynamics, Physical Review B, vol.2015, issue.20, 2015. ,
DOI : 10.1103/PhysRevLett.111.210402
Entanglement Entropy and the Fermi Surface, Physical Review Letters, vol.105, issue.5, 2010. ,
DOI : 10.1103/PhysRevB.78.205116
Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior, pp.37-39, 0202. ,
DOI : 10.1017/CBO9781139046213
Multipartite entanglement and high-precision metrology, Physical Review A, vol.1, issue.2, p.220, 2012. ,
DOI : 10.1103/PhysRevLett.99.250405
Notes on black-hole evaporation, Physical Review D, vol.13, issue.4, pp.870-892, 1976. ,
DOI : 10.1103/PhysRevD.13.2720
The role of relative entropy in quantum information theory, Reviews of Modern Physics, vol.60, issue.1, pp.197-234, 2002. ,
DOI : 10.1103/PhysRevA.60.2746
Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Physical Review A, vol.6, issue.8, pp.4277-4281, 1989. ,
DOI : 10.1007/978-3-642-86751-4
Information Contents of Distributions, 1963. ,
Algorithm 923, ACM Transactions on Mathematical Software, vol.38, issue.4, pp.1-3017, 2012. ,
DOI : 10.1145/2331130.2331138
Squeezed atomic states and projection noise in spectroscopy, Physical Review A, vol.65, issue.1, pp.67-88, 1994. ,
DOI : 10.1103/PhysRevLett.65.2347
Quantum Measurement and Control, p.9780521804424, 2010. ,
DOI : 10.1017/CBO9780511813948
Violation of the Entropic Area Law for Fermions, Physical Review Letters, vol.19, issue.1, 2006. ,
DOI : 10.1016/j.physleta.2005.01.060
Entanglement temperature and entanglement entropy of excited states, Journal of High Energy Physics, vol.245, issue.12, pp.140-150, 2013. ,
DOI : 10.1006/aphy.1996.0007
Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors, Reviews of Modern Physics, vol.7, issue.4, pp.694-704, 1962. ,
DOI : 10.1103/PhysRevLett.7.162
Determining the speed of multipartite quantum systems by few local measurements, 2016. ,
Recherches sur la théorie des Quanta " . Theses. URL: https : / / tel . archives -ouvertes, p.6807, 1924. ,