Perfect controlled bidirectional remote implementation of general unitary operators via a partially hyperentangled state

We design a new quantum circuit to generate a five-photon maximal slice state, which is partially hyperentangled in two degrees of freedom. This state is then employed as a shared quantum channel for a protocol of controlled bidirectional remote implementation of general unitary operators. In our protocol, the parameters characteristic of the quantum channel is known exclusively by the controller, Charlie; as a result, only she is able to act appropriately to decide on the completion of the protocol. The merits of our protocol are twofold: First, it extends the ability of bidirectional remote implementation of partially unknown quantum operators to general unknown unitary ones, and second, the proposed two-way common control based on hyperentanglement requires fewer resources than two one-way separate controls based on conditional entanglements do. Remarkably, our protocol is perfect (i.e., achieving a success probability and fidelity of 1), yet this perfection is independent of the quantum channel parameters (i.e., it is insensitive to the channel’s entanglement degree).