Encoding and decoding in complementary bases with quantum gates

The total information content of a composite system consisting of k qubits can either be completely encoded in a specific computational basis, or alte rnatively it can be partially encoded in a number of different bases. In th at case the information encoded in a complete set of mutually complementary bases is again k bits. Using only two single-qubit gates and the controlle d-NOT gate, one can implement coding and decoding in such a complete set. T he total information content is then invariant under the particular choice of a complete set of mutually complementary bases. For maximally entangled states the k bits of information are not encoded into the k qubits separate ly but only into their joint properties.