 Amplitude damping channel

A zero-temperature energy-relaxation channel transfers the excited population of a qubit to its ground state. Its Kraus operators are $A_0=\mathrm{diag}(1,\sqrt{1-p})$ and $A_1=\sqrt{p}|0⟩⟨1|$ for $0\le p\le 1$. They satisfy ${\sum }_j{A}_j^{†}{A}_j=I$. The excited population is multiplied by $1-p$ and coherences by $\sqrt{1-p}$. For nonzero $p$, it is not a unital quantum channel.

The amplitude damping channel is a type of quantum channel that models a common form of quantum noise. It represents a particular kind of decoherence that can occur in quantum systems, especially relevant to quantum computing and quantum information theory. In more technical terms, the amplitude damping channel describes the process by which a quantum state behaves similarly to the way a dissipative system loses energy.