An antiunitary operator between complex Hilbert spaces is a surjective antilinear map satisfying the displayed inner product identity. It preserves norms but conjugates scalars. In a chosen orthonormal basis it is , with a unitary operator and coefficientwise complex conjugation. Conversely any such is antiunitary. Antilinearity by itself does not preserve norms.
An antiunitary operator is a type of linear operator that is an essential concept in quantum mechanics and quantum information theory. It has properties that distinguish it from unitary operators, which are commonly associated with the evolution of quantum states.
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