Properties of Quantum Languages

The class of quantum languages Q(Σ) over an alphabet Σ is the class of languages accepted by quantum automata. We study properties of Q(Σ) and compare Q(Σ) with the class of regular languages R(Σ). It is shown that Q(Σ) is closed under union, intersection, and reversal but is not closed under complementation, concatenation, or Kleene star. It is also shown that Q(Σ) and R(Σ) are incomparable. Finally, we prove that L ∈ Q(Σ) if and only if L admits a transition amplitude function satisfying a certain property and a similar characterization is given for R(Σ).

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