2018 - Fellow of the American Mathematical Society For contributions to quantum information theory and coding theory, the theory of random matrices, the study of special functions, non-commutative geometry and number theory.
Eric M. Rains mainly investigates Combinatorics, Discrete mathematics, Linear code, Pure mathematics and Invariant. He has included themes like Quantum information science, Quantum entanglement and Subsequence in his Combinatorics study. The Discrete mathematics study combines topics in areas such as Longest increasing subsequence, Fixed point, Classical group and Algebraic number.
His Linear code study combines topics from a wide range of disciplines, such as Invariant theory and Algebra. In the subject of general Pure mathematics, his work in Rational function and Hypergeometric distribution is often linked to Probability theory and Aztec diamond, thereby combining diverse domains of study. The various areas that he examines in his Quantum convolutional code study include Stabilizer code, Concatenated error correction code, Quantum capacity and Decoherence-free subspaces.
The scientist’s investigation covers issues in Pure mathematics, Combinatorics, Discrete mathematics, Algebra and Macdonald polynomials. His Pure mathematics research is multidisciplinary, incorporating elements of Eigenvalues and eigenvectors and Mathematical analysis. Eric M. Rains combines subjects such as Classical group and Matrix, Unitary matrix with his study of Eigenvalues and eigenvectors.
His study in Combinatorics is interdisciplinary in nature, drawing from both Type, Invariant and Group. His Discrete mathematics study combines topics in areas such as Invariant theory, Quantum, Linear programming and Quantum codes, Linear code. His Linear code research incorporates themes from Hamming code and Concatenated error correction code.
Eric M. Rains mostly deals with Pure mathematics, Moduli space, Macdonald polynomials, Type and Lax pair. His Macdonald polynomials research is under the purview of Combinatorics. His work deals with themes such as Higgs boson and Riemann surface, which intersect with Combinatorics.
His Type research incorporates elements of Hypergeometric function, Gravitational singularity, Quantization, Star product and Orthogonal polynomials. To a larger extent, he studies Discrete mathematics with the aim of understanding Natural transformation. His Discrete mathematics research is multidisciplinary, incorporating perspectives in Affine group, Quantum affine algebra and Affine Hecke algebra.
His primary areas of investigation include Pure mathematics, Lax pair, Moduli space, Macdonald polynomials and Affine transformation. His Pure mathematics study frequently intersects with other fields, such as Generalization. His studies in Lax pair integrate themes in fields like Symmetry, Linear system, Differential and Symmetric difference.
His Moduli space research includes elements of Combinatorics, Riemann surface, Space, Polynomial and Higgs boson. His biological study spans a wide range of topics, including Hypergeometric function, Type, Bounded function, Partial fraction decomposition and Symplectic geometry. His work in Affine transformation addresses subjects such as Interpolation, which are connected to disciplines such as Kernel.
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Quantum error correction via codes over GF(4)
A.R. Calderbank;E.M. Rains;P.M. Shor;N.J.A. Sloane.
international symposium on information theory (1997)
Quantum nonlocality without entanglement
Charles H. Bennett;David P. DiVincenzo;Christopher A. Fuchs;Tal Mor.
Physical Review A (1999)
Quantum Error Correction and Orthogonal Geometry
A. R. Calderbank;E. M. Rains;P. W. Shor;N. J. A. Sloane.
Physical Review Letters (1997)
Nonbinary quantum codes
IEEE Transactions on Information Theory (1999)
E. M. Rains;N. J. A. Sloane.
arXiv: Combinatorics (2002)
A semidefinite program for distillable entanglement
IEEE Transactions on Information Theory (2001)
Shadow bounds for self-dual codes
IEEE Transactions on Information Theory (1998)
Transformations of elliptic hypergeometric integrals
Eric M. Rains.
Annals of Mathematics (2010)
Bound on distillable entanglement
E. M. Rains.
Physical Review A (1999)
Eynard–Mehta Theorem, Schur Process, and their Pfaffian Analogs
Alexei Borodin;Eric M. Rains.
Journal of Statistical Physics (2005)
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