Weak Multiplicativity for Random Quantum Channels

[1]  David Pérez-García,et al.  Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy , 2012, 1201.6324.

[2]  Ashley Montanaro,et al.  Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization , 2010, JACM.

[3]  Ion Nechita,et al.  The absolute positive partial transpose property for random induced states , 2011, 1108.1935.

[4]  Matthias Christandl,et al.  Entanglement of the Antisymmetric State , 2009, 0910.4151.

[5]  B. Collins,et al.  Towards a state minimizing the output entropy of a tensor product of random quantum channels , 2011, 1111.6269.

[6]  Teodor Banica,et al.  Asymptotic Eigenvalue Distributions of Block-Transposed Wishart Matrices , 2011, 1105.2556.

[7]  Ion Nechita,et al.  Random quantum channels II: Entanglement of random subspaces, Rényi entropy estimates and additivity problems , 2009, 0906.1877.

[8]  Guillaume Aubrun,et al.  Partial transposition of random states and non-centered semicircular distributions , 2010, 1011.0275.

[9]  Matthias Christandl,et al.  Highly entangled states with almost no secrecy. , 2010, Physical review letters.

[10]  Ion Nechita,et al.  Eigenvalue and Entropy Statistics for Products of Conjugate Random Quantum Channels , 2010, Entropy.

[11]  Jonathan Novak,et al.  Primitive factorizations, Jucys-Murphy elements, and matrix models , 2010, 1005.0151.

[12]  Guillaume Aubrun,et al.  Hastings’s Additivity Counterexample via Dvoretzky’s Theorem , 2010, 1003.4925.

[13]  Aram W. Harrow,et al.  An efficient test for product states , 2010 .

[14]  Ashley Montanaro,et al.  An Efficient Test for Product States with Applications to Quantum Merlin-Arthur Games , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[15]  M. Horodecki,et al.  Constructive counterexamples to the additivity of the minimum output Rényi entropy of quantum channels for all p > 2 , 2009, 0911.2515.

[16]  Ion Nechita,et al.  Random Quantum Channels I: Graphical Calculus and the Bell State Phenomenon , 2009, 0905.2313.

[17]  Jonathan Novak Jucys-Murphy elements and the unitary Weingarten function , 2010 .

[18]  S. Matsumoto,et al.  Unitary Matrix Integrals, Primitive Factorizations, and Jucys-Murphy Elements , 2010 .

[19]  Ion Nechita,et al.  Gaussianization and eigenvalue statistics for random quantum channels (III) , 2009 .

[20]  Guillaume Aubrun,et al.  Non-additivity of Renyi entropy and Dvoretzky's Theorem , 2009, 0910.1189.

[21]  S. Matsumoto,et al.  Jucys-Murphy Elements and Unitary Matrix Integrals , 2009, 0905.1992.

[22]  M. Hastings Superadditivity of communication capacity using entangled inputs , 2009 .

[23]  Keiji Matsumoto,et al.  Quantum Merlin-Arthur Proof Systems: Are Multiple Merlins More Helpful to Arthur? , 2003, Chic. J. Theor. Comput. Sci..

[24]  Andreas J. Winter,et al.  Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p > 1 , 2008, ArXiv.

[25]  Aram W. Harrow,et al.  Counterexamples to Additivity of Minimum Output p-Rényi Entropy for p Close to 0 , 2007, 0712.3628.

[26]  Patrick Hayden,et al.  The maximal p-norm multiplicativity conjecture is false , 2007, 0707.3291.

[27]  Andreas Winter,et al.  The maximum output p-norm of quantum channels is not multiplicative for any p>2 , 2007, 0707.0402.

[28]  Alexandru Nica,et al.  Lectures on the Combinatorics of Free Probability , 2006 .

[29]  B. Collins,et al.  Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group , 2004, math-ph/0402073.

[30]  Koenraad M. R. Audenaert A Digest on Representation Theory of the Symmetric Group , 2006 .

[31]  P. Shor Equivalence of Additivity Questions in Quantum Information Theory , 2003, quant-ph/0305035.

[32]  Alexander Semenovich Holevo,et al.  On the Multiplicativity Hypothesis for Quantum Communication Channels , 2003 .

[33]  B. Collins Moments and cumulants of polynomial random variables on unitarygroups, the Itzykson-Zuber integral, and free probability , 2002, math-ph/0205010.

[34]  R. Werner,et al.  Counterexample to an additivity conjecture for output purity of quantum channels , 2002, quant-ph/0203003.

[35]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[36]  A. Holevo,et al.  On the multiplicativity conjecture for quantum channels , 2001, math-ph/0103015.

[37]  R. Werner,et al.  On Some Additivity Problems in Quantum Information Theory , 2000, math-ph/0003002.

[38]  Philippe Biane,et al.  Some properties of crossings and partitions , 1997, Discret. Math..

[39]  N. M. Adrianov An analog of the Harer-Zagier formula for unicellular bicolored maps , 1997 .