We show how a CNOT gate and single-qubit rotation can be implemented non-locally,We also report on the quantitative relations between these quantum actions,entanglement and classical communication resources required in the implementation.
We present two optimal schemes for non-local implementing a single-qubit rotation operation via a maxi-mally entangled quantum channel. We report on the quantitative relations between the quantum action,entangled and classical communication resources required in the implementation. We also put forward twoschemes for conclusive implementing the non-local quantum single-qubit rotation via a partially entangledquantum channel. Both these methods can appropriately be referred to as qubit-assisted processes.
We prove that a generic three-qubit quantum logic gate can be implemented using at most 98 one-qubit rotations about the y- and z-axes and 40 CNOT gates, beating an earlier bound of 64 CNOT gates.
Single qubit rotation gate and the controlled-NOT (CNOT) gate constitute a complete set of gates for universal quantum computation. In general the CNOT gate are only for two nearby qubits. For two qubits which are remote from each other, we need a series of swap gates to transfer these two qubits to the nearest neighboring sites, and then after the CNOT gate we should transfer them to their original sites again. However, a series of swap gates are resource for quantum information processing. One economy way which does not consume so much resource is to implement CNOT gate remotely. The remote CNOT gate is to implement the CNOT gate for two remotely separated qubits with the help of one additional maximally entangled state. The original remote CNOT gate is for two qubits, here we will present the d-dimensional remote CNOT gate. The role of quantum teleportation is identified in the process of the remote CNOT gate.