Gate teleportation using Series entanglement distributions on arbitrary remote states

The counter-intuitive and one of the most striking features of the quantum world is entanglement, which has found practical use in the eld of communication and cryptography. Various quantum communication protocols, like qubit teleportation, superdense coding, quantum information splitting, secret sharing, remote state preparation have been theoretically and experimentally demonstrated through entangled channels. Gate teleportation is another important protocol implementing a multi-partite quantum gates between qubits, which are spatially distributed. The protocol requires application of a unitary gate, that can not be decomposed into individual local operations i.e., |ψ〉AB −→ U|ψ〉AB, where U 6= UA ⊗ UB. This can be achieved using entangled channels shared by the remote parties. In the context of distributed quantum computing, it is necessary to produce controlled operations between remote parties, which may be more than two in number. Together with the local single particle operations, these can produce the necessary entanglement between remote parties for implementation of quantum tasks. In the familiar network [1], each of the control parties shares one entangled state with the target party and none of the control parties shares entanglement between them whereas in series network, the entanglement distribution forms a series, such that the control parties share entanglement with the adjacent control parties and only one of them shares entanglement with the target party. As this network is linear, the target party has to maintain only one entangled channel. It is particularly useful when the entanglement sharing is di cult between each controlling agent with the target party. The paper is organized as follows. We start with a three party scenario, where Alice and Bob simultaneously teleport controlled-Hermitian gate to Charlie in series entangled network, which is then generalized for arbitrary multi-partite state. Sect. II deals with the teleportation of controlled-controlled-Unitary gate and the generalization to n-controlled Unitary gate teleportation. Sect. III is devoted to conclusion and directions for future work.