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Résumé : We discuss BB84 quantum key distribution protocol in light of quantum algorithmic information. While Shannon's information theory needs a probability to define a notion of information, algorithmic information theory does not need it and can assign a notion of information to an individual object. The theory regards a program length necessary to describe an object, Kolmogorov complexity, as the most fundamental quantity. Recently, its quantum versions were proposed by a several researchers. We employ a definition of quantum Kolmogorov complexity given by Vitanyi. A goal of the quantum key distribution is to distribute a random binary sequence only between legitimate users. In the context of quantum algorithmic complexity, a security criterion is formulated with the quantum Kolmogorov complexity. We show that a simple BB84 protocol indeed distribute a binary sequence between Alice and Bob that looks almost random for Eve in a probability exponentially close to 1.