A quantum channel is a linear, completely positive, trace-preserving map taking input density operators to output density operators. Trace preservation keeps total probability one. Complete positivity requires positivity even when the map acts on one part of an entangled larger system, with the other part unchanged.
In finite dimensions, a Kraus representation writes , with . A unitary channel has one Kraus operator; a dephasing channel suppresses coherences in a specified basis. Different physical implementations can yield the same channel after unobserved degrees of freedom are traced out. A conditional measurement outcome alone is generally trace decreasing; only the sum over all outcomes gives a trace-preserving channel.
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.
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