Quantum Algorithmic Information Theory

The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capable of arbitrary U(2) transformations. Basic to all these considerations is quantum theory, which is most conveniently expressible in Hilbert space. 1 Information is physical, so is computation The reasoning in constructive mathematics [16, 19, 20] and recursion theory, at least insofar as their applicability to worldly things is concerned, makes implicit assumptions about the operationalizability of the entities of discourse. It is this postulated correspondence between practical and theoretical ..