Quantum depolarizing channel
A quantum depolarizing channel is a model for quantum noise in quantum systems. The -dimensional depolarizing channel can be viewed as a completely positive trace-preserving map , depending on one parameter , which maps a state onto a linear combination of itself and the maximally mixed state, . The condition of complete positivity requires to satisfy the bounds . Qubit Channel The single qubit depolarizing channel has operator-sum representation on a density matrix given by where are the Kraus operators given by and are the Pauli matrices. The trace preserving condition is satisfied by the fact that Geometrically the depolarizing channel can be interpreted as a uniform contraction of the Bloch sphere, parameterized by . In the case where the channel returns the maximally-mixed state for any input state , which corresponds of the complete contraction of the Bloch-sphere down to the single-point given by the origin. Classical capacity The HSW theorem states that the classical capacity of a quantum channel can be characterized as its regularized Holevo information: This quantity is difficult to compute and this reflects our ignorance on quantum channels. However, if the Holevo information is additive for a channel , i.e., Then we can get its