The operator-sum-difference representation of a quantum noise channel
Quantum Information Processing
On account of the Abel-Galois no-go theorem for the algebraic solution to quintic and higher order polynomials, the eigenvalue problem and the associated characteristic equation for a general noise dynamics in dimension d via the Choi-Jamiolkowski approach cannot be solved in general via radicals. We provide a way around this impasse by decomposing the Choi matrix into simpler, not necessarily positive, Hermitian operators that are diagonalizable via radicals, which yield a set of 'positive'
... 'negative' Kraus operators. The price to pay is that the sufficient number of Kraus operators is d^4 instead of d^2, sufficient in the Kraus representation. We consider various applications of the formalism: the Kraus repesentation of the 2-qubit amplitude damping channel, the noise resulting from a 2-qubit system interacting dissipatively with a vacuum bath; defining the maximally dephasing and purely dephasing components of the channel in the new representation, and studying their entanglement breaking and broadcast properties.