For normalized maximally entangled , the Choi matrix of is . Choi's theorem says is completely positive exactly when .
A random unitary channel has . Its Choi matrix is a convex combination of maximally entangled pure states.
A quantum channel is unital when . Every random unitary channel is unital, while the converse fails in dimension at least three.
The Werner–Holevo channel is . Its normalized Choi matrix is the maximally mixed state on the antisymmetric subspace.
A quantum channel is strictly contractive in trace distance when it reduces the distance between every pair of distinct density operators by a uniform factor smaller than one.
A finite-dimensional quantum channel is primitive when some power maps every nonzero positive operator to a positive-definite operator. Equivalently, eigenvalue one is simple and no other eigenvalue lies on the unit circle.
A Stinespring dilation represents a quantum channel by an isometry followed by tracing out the environment.
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A quantum channel is a mathematical model used in quantum information theory to describe the transmission of quantum information between two parties, typically referred to as the sender (or Alice) and the receiver (or Bob). It represents a medium through which quantum states can be sent, allowing the transfer of quantum bits or qubits. Quantum channels account for the effects of noise and loss in the transmission of quantum information, which can arise from interactions with the environment or imperfections in the communication process.