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Note on generalized quantum gates and quantum Operations. (English) Zbl 1160.81350
Summary: Recently, Gudder proved that the set of all generalized quantum gates coincides the set of all contractions in a finite-dimensional Hilbert space S. Gudder [Int. J. Theor. Phys. 47, No. 1, 268–279 (2008; Zbl 1145.81020)]. In this note, we proved that the set of all generalized quantum gates is a proper subset of the set of all contractions on an infinite dimensional separable Hilbert space \(\mathcal H\). Meanwhile, we proved that the quantum operation deduced by an isometry is an extreme point of the set of all quantum operations on \(\mathcal H\).

MSC:
81P68 Quantum computation
81P15 Quantum measurement theory, state operations, state preparations
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