Representations of the multi-qubit Clifford group

The Clifford group is a fundamental structure in quantum information with a wide variety of applications. We discuss the tensor representations of the q-qubit Clifford group, which is defined as the normalizer of the q-qubit Pauli group in U\(2^q\). In particular, we characterize all irreducible subrepresentations of the two-copy representation varphi^otimes2 of the Clifford group on the matrix space mathbb{C}^{dtimes d}otimes mathbb{C}^{dtimes d} with d=2^q. In an upcoming companion paper we applied this result to cut down the number of samples necessary to perform randomised benchmarking, a method for characterising quantum systems.