A mathematical description of the evolution of a quantum system, including noise and decoherence processes.A quantum channel is a mathematical object that describes how a quantum system evolves, including the effects of noise, decoherence, and information loss. In the ideal world of quantum mechanics, systems evolve in a perfectly reversible, unitary way — like a clean wave propagating without disturbance. But in reality, any interaction with the environment introduces noise, and a quantum channel captures this messy, irreversible evolution in a precise, operator-based formalism.
The formal concept of quantum channels was developed in the 1970s and 1980s, building on the work of Kraus, Stinespring, and others in the theory of completely positive maps. The term 'quantum channel' became standard with the rise of quantum information theory.
A quantum channel is a completely positive, trace-preserving map acting on the density matrix of a quantum system. It takes an input state and produces an output state, possibly mixed, reflecting the influence of the environment. The channel can be represented as a sum of Kraus operators, which encode both the desired evolution and the noise processes, such as amplitude damping or phase flip.
Quantum channels are essential in quantum error correction, where they model the noise that must be corrected, and in quantum cryptography, where they describe the transmission of quantum states through imperfect communication lines.
A quantum channel can be used to simulate any physical process that a quantum system undergoes, from a single photon passing through a fiber optic cable to the decoherence of a qubit in a quantum computer.
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