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Hypercontractive inequalities have become important tools in theoretical computer science and have recently found applications in quantum computation.
On bounded bilinear forms in an infinite number of variables
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On the absolute convergence of Dirichlet series
H. Bohnenblust and E. Hille · 1931
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Proposed experiment to test local hidden-variable theories
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Étude des coefficients Fourier des fonctiones de Lp(G)
A. Bonami · 1970
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Fourier analysis on Euclidean spaces
E. Stein and G. Weiss · 1971
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Hypercontractive semigroups and two dimensional self-coupled Bose fields
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Statistical decision theory for quantum systems
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Inequalities in Fourier analysis
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Logarithmic Sobolev inequalities
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Quantum detection and estimation theory
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The influence of variables on Boolean functions
J. Kahn, G. Kalai, and N. Linial · 1988
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Sobolev inequalities, the Poisson semigroup, and analysis on the sphere S n S^{n}
W. Beckner · 1992
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Hypercontractivity: a bibliographic review
E. B. Davies, L. Gross, and B. Simon · 1992
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Optimal hypercontractivity for Fermi fields and related non-commutative integration inequalities
E. Carlen and E. Lieb · 1993
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Communication complexity and quasi randomness
F. Chung and P. Tetali · 1993
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The fourth moment method
B. Berger · 1997
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Free hypercontractivity
P. Biane · 1997
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Gaussian Hilbert spaces
S. Janson · 1997
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The probabilistic method
N. Alon and J. Spencer · 2000
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Analysis in integer and fractional dimensions
R. Blei · 2001
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On the distribution of the Fourier spectrum of Boolean functions
J. Bourgain · 2002
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Consequences and limits of nonlocal strategies
R. Cleve, P. Høyer, B. Toner, and J. Watrous · 2004
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Gaussian quantum fluctuations in interacting many particle systems
M. Hartmann, G. Mahler, and O. Hess · 2004
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Remote preparation of quantum states
C. H. Bennett, P. Hayden, D. Leung, P. Shor, and A. Winter · 2005
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Analytical methods in combinatorics and computer-science, 2005
I. Dinur and E. Friedgut · 2005
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Multiplayer XOR games and quantum communication complexity with clique-wise entanglement, 2009
J. Briët, H. Buhrman, T. Lee, and T. Vidick · 2009
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Notes on spherical harmonics and linear representations of Lie groups, 2009
J. Gallier · 2009
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W. Matthews, S. Wehner, and A. Winter · 2009
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Coordinatewise multiple summing operators in Banach spaces
A. Defant, D. Popa, and U. Schwarting · 2010
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An efficient test for product states, with applications to quantum Merlin-Arthur games
A. Harrow and A. Montanaro · 2010
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Hadamard tensors and lower bounds on multiparty communication complexity
J. Ford and A. Gál · 2005
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Approximating the cut-norm via Grothendieck’s inequality
N. Alon and A. Naor · 2006
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Hypercontractivity, logarithmic Sobolev inequalities, and applications: a survey of surveys
L. Gross · 2006
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Random measurement bases, quantum state distinction and applications to the hidden subgroup problem
P. Sen · 2006
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Quantum t-designs: t-wise independence in the quantum world
A. Ambainis and J. Emerson · 2007
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On the Fourier tails of bounded functions over the discrete cube
I. Dinur, E. Friedgut, G. Kindler, and R. O’Donnell · 2007
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A. Montanaro and T. Osborne · 2010
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Noise stability of functions with low influences: Invariance and optimality
E. Mossel, R. O’Donnell, and K. Oleszkiewicz · 2010
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The need for structure in quantum speedups
S. Aaronson and A. Ambainis · 2011
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Explicit lower and upper bounds on the entangled value of multiplayer XOR games, 2011
J. Briët and T. Vidick · 2011
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Near-optimal and explicit Bell inequality violations
H. Buhrman, O. Regev, G. Scarpa, and R. de Wolf · 2011
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Quantum one-way communication can be exponentially stronger than classical communication
B. Klartag and O. Regev · 2011
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How low can approximate degree and quantum query complexity be for total boolean functions?, 2012
A. Ambainis and R. de Wolf · 2012
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The asymptotic growth of the constants in the Bohnenblust-Hille inequality is optimal
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Distinguishing multi-partite states by local measurements, 2012
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On the growth of the optimal constants of the multilinear Bohnenblust-Hille inequality, 2012
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New upper bounds for the constants in the Bohnenblust-Hille inequality
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