function varargout = maxEfrac(rho) % maxEfrac Maximum entangled fraction % requires: unpauli.m % author: Toby Cubitt % license: GPL2 % % S = maxEfrac(RHO) returns the maximum entangled fraction (also % known as maximum singlet fraction) of 2x2 density matrix RHO, % defined as the % % max phi'*rho*phi % % where phi is a two-qubit maximally entangled state % % [O1,S,O2] = maxEfrac(RHO) in addition returns the orthogonal % matrices that achieve the maximum in the Hilbert-Schmidt % representation. %% Copyright (C) 2004-2009 Toby Cubitt %% %% This program is free software; you can redistribute it and/or %% modify it under the terms of the GNU General Public License %% as published by the Free Software Foundation; either version 2 %% of the License, or (at your option) any later version. %% %% This program is distributed in the hope that it will be useful, %% but WITHOUT ANY WARRANTY; without even the implied warranty of %% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the %% GNU General Public License for more details. %% %% You should have received a copy of the GNU General Public License %% along with this program; if not, write to the Free Software %% Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, %% MA 02110-1301, USA. R = pauli(rho); T = abs(R(2:4,2:4)).*sign(real(R(2:4,2:4))); [O1,S,O2] = svd(T); S = diag([1,1,det(O1)])*S*diag([1,1,det(O2)]); O1 = O1*diag([1,1,det(O1)]); O2 = O2*diag([1,1,det(O2)]); Q = (O2*diag([1,1,-1])*O1.').'; P(1,1) = 1; P(2:4,2:4) = Q; phi = unpauli(P); varargout{1} = trace(phi*rho); if nargout >= 2 varargout{2} = phi; end if nargout == 4 varargout{3} = O1; varargout{4} = O2; end