Schematic representation of the quantum dual signature scheme. The signatory Alice first signs messages 1 and 2 which are required to be received by Bob and Charlie, respectively. Then she combines the two signatures into a dual signature and sends it to the verifier Bob. Bob verifies the part of the quantum dual signature which is related to message 1 and transmits the rest of the dual signature to Charlie. Subsequently, Charlie completes the verification for the signature of message 2. PS and BS are phase shifter and beam splitter, respectively. The U box stands for performing unitary operations.