Remote Preparation of an Arbitrary Two-Qubit State with Three-Party

Abstract

In this paper, we propose a scheme to remotely prepare an arbitrary two-qubit state from one sender to either of two receivers. Two cases of the prepared quantum state, an arbitrary two-qubit state with real coefficients and complex coefficients, are considered. Firstly, one single EPR pair and a GHZ state are used as the quantum channel. Then the present scheme is extended to some partially entangled states as the quantum channel. To design these schemes, some useful and general measurement bases have been constructed. The successful probability and classical communication cost of these schemes are also calculated to weigh the efficiency and cost.

Controlled Remote Preparation of a Two-Qubit State via Positive Operator-Valued Measure and Two Three-Qubit Entanglements

“…Moreover, we have also explored the applications of the scheme to some special ensembles of states in detail, and the corresponding success probabilities in different cases are also calculated, which show that for theses special state to be prepared, the remote preparation can be achieved with higher probability. Comparing with the previous two-qubit RSP schemes [25,44,45,47,[50][51][52]54], the present one has the following advantages. First, the quantum channels are different in forms.…”

“…First, the quantum channels are different in forms. In this present scheme, a GHZ-type state and a W-type state are used as the shared quantum channel, whereas the quantum channels in the previous schemes were composed of Einstein-Podolsky-Rosen (EPR) pairs, GHZ states, or their modified versions [25,44,45,47,50,54]. Second, different from the previous RSP schemes [25,44,45,[50][51][52]54], in which the usual PM was used to realize the probabilistic remote preparation, we employ the method of POVM, instead of the usual PM, to finally restore the state to be prepared in this protocol.…”

“…In this present scheme, a GHZ-type state and a W-type state are used as the shared quantum channel, whereas the quantum channels in the previous schemes were composed of Einstein-Podolsky-Rosen (EPR) pairs, GHZ states, or their modified versions [25,44,45,47,50,54]. Second, different from the previous RSP schemes [25,44,45,[50][51][52]54], in which the usual PM was used to realize the probabilistic remote preparation, we employ the method of POVM, instead of the usual PM, to finally restore the state to be prepared in this protocol. Third, this protocol has not only investigated the RSP of an arbitrary two-qubit state, but also explored its applications to some special ensembles of states in detail, while the previous RSP schemes only considered the RSP of a general two-qubit state or a class of two-qubit states [25,44,45,47,51,52,54].…”

“…Second, different from the previous RSP schemes [25,44,45,[50][51][52]54], in which the usual PM was used to realize the probabilistic remote preparation, we employ the method of POVM, instead of the usual PM, to finally restore the state to be prepared in this protocol. Third, this protocol has not only investigated the RSP of an arbitrary two-qubit state, but also explored its applications to some special ensembles of states in detail, while the previous RSP schemes only considered the RSP of a general two-qubit state or a class of two-qubit states [25,44,45,47,51,52,54]. Nowadays, three-photon entanglement has been observed and used to verify quantum nonlocality [62,63], a number of feasible protocols for generating GHZ states as well as various theoretical and experimental schemes for generating the W state have been proposed [64][65][66][67].…”

“…In terms of entanglements in quantum channels, these RSP schemes can be classified into two types. One uses maximally entangled states [23,24,28,34,43,44,[50][51][52][53][54] while another utilizes non-maximally entangled states [25-27, 29, 30, 36, 45, 47, 49]. In the latter case, usually one or more auxiliary qubits need to be incorporated and entangled with the original qubits.…”