Remote state preparation without oblivious conditions

Abstract

In quantum teleportation, neither Alice nor Bob acquires any classical knowledge on teleported states. The teleportation protocol is said to be oblivious to both parties. In remote state preparation (RSP) it is assumed that Alice is given complete classical knowledge on the state that is to be prepared by Bob. Recently, Leung and Shor [8] showed that the same amount of classical information as that in teleportation needs to be transmitted in any exact and deterministic RSP protocol that is oblivious to Bob. We study similar RSP protocols, but not necessarily oblivious to Bob. First it is shown that Bob's quantum operation can be safely assumed to be a unitary transformation. We then derive an equation that is a necessary and sufficient condition for such a protocol to exist. By studying this equation, we show that one qubit RSP requires 2 cbits of classical communication, which is the same amount as in teleportation, even if the protocol is not assumed oblivious to Bob. For higher dimensions, it is still open whether the amount of classical communication can be reduced by abandoning oblivious conditions.

Faithful remote state preparation using finite classical bits and a nonmaximally entangled state

“…(3) is a necessary condition for such RSP protocols. It is also a sufficient condition [9,12], because Alice only needs to apply a measurement on her system A with POVM operators…”

Deterministic remote preparation of an arbitrary qubit state using a partially entangled state and finite classical communication

“…For example, the first RSP scheme proposed by Pati [4] uses a Bell state, realizing deterministic preparation of a qubit from a fixed great circle on the Bloch sphere. Other later proposed schemes extended the preparable ensembles to varying degrees for preparing more general qubits, like deterministic preparations of arbitrary pure qubits [8][9][10], probabilistic preparations of arbitrary qubits [10,11], and more resently, schemes for deterministic preparations of arbitrary qubits were also implemented [12,13]. Unfortunately, these mentioned schemes are unadaptable to partially entangled resource states, which may occur in the real world.…”

Secret key sharing using entanglement swapping and remote preparation of quantum state

“…After that, many researchers studied and proposed different theoretical types of RSP [17][18][19][20][21][22][23][24] . On the other hand, Peng et al [19] have implement RSP using Nuclear magnetic resonance and Xiang et al [21] have implemented RSP using spontaneous parametric down-conversion, single photon detector and linear optical elements.…”