Remote interactions on distributed quantum systems: non-local conditional operations and production of multiparticle entangled state

We present a systematic simple method for constructing non-local quantum conditional rotation with single target and multiple targets operations. We firstly show how a non-local conditional rotation with single target operation can be implemented with unit fidelity and unit probability by using a maximally entangled pair as quantum channel. We also put forward a scheme for probabilistically implementing the operation with unit fidelity by employing a partially entangled pair as quantum channel. The required physical resources for implementation of the non-local operation in these two cases are discussed. We further consider non-local conditional rotation with multiple targets operations on N spatially distributed systems, and show that the number of possible distinct operations increases here exponentially, with the available number of entangled pairs that are initially distributed between systems. We also point out that the non-local conditional rotation operation can be used to generate multiparticle entanglement between particles belonging to distant users in a communication network and distributed quantum computer.