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On swapping the states of two qudits (1101.4159v1)
Published 21 Jan 2011 in quant-ph
Abstract: The SWAP gate has become an integral feature of quantum circuit architectures and is designed to permute the states of two qubits through the use of the well-known controlled-NOT gate. We consider the question of whether a two-qudit quantum circuit composed entirely from instances of the generalised controlled-NOT gate can be constructed to permute the states of two qudits. Arguing via the signature of a permutation, we demonstrate the impossibility of such circuits for dimensions $d \equiv 3$ (mod 4).