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Chinese Journal of Quantum Electronics

Probabilistic remote preparation of a bipartite three-dimensional equatorial entangled state

You-Bang Zhan

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

With two qutrit states of non-maximally entangled particles as the quantum channel,a protocol for the probabilistic remote reparation of a bipartite three-dimensional equatorial entangled state is proposed. It is found that a bipartite qutrit orthogonal projective measurement,an auxiliary qutrit particle and corresponding unitary transformation are required.

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With two qutrit states of non-maximally entangled particles as the quantum channel,a protocol for the probabilistic remote reparation of a bipartite three-dimensional equatorial entangled state is proposed. It is found that a bipartite qutrit orthogonal projective measurement,an auxiliary qutrit particle and corresponding unitary transformation are required.
We present a scheme for probabilistic remote preparation of a tripartite qutrit entangled state with a partial tripartite qutrit entangled state and a partial bipartite qutrit entangled state as the quantum channel. It is found that a bipartite qutrit orthogonal projective measurement, an auxiliary qutrit particle, and the corresponding unitary transformation are required. A scheme for probabilistic remote preparation of a tripartite qudit equatorial entangled state by using a partial tripartite qudit entangled state and a partial bipartite qudit entangled state as the quantum channel is also proposed. We calculate the successful total probability and the total classical communication cost required in the RSP process, respectively.
A scheme for probabilistic remotely preparing N-particle d-dimensional equatorial entangled states via entangled swapping with three parties is presented. The quantum channel is composed of N – 1 pairs of bipartite d-dimensional non-maximally entangled states and a tripartite d-dimension non-maximally entangled state. It is shown that the sender can help either of the two receivers to remotely prepare the original state, and the N-particle projective measurement and the generalized Hadamard transformation are needed in this scheme. The total success probability and classical communication cost are calculated.
We propose some schemes for remote preparation of arbitrary high-dimensional equatorial entangled state via a single bipartite high-dimensional entangled state as quantum channel. We firstly present the remote preparation of bipartite three- and d-dimensional equatorial entangled state by using a single entangled qutrit and qudit pair, respectively, and then directly generalize the schemes to multipartite case. The cases of the quantum channel being non-maximally two-qutrit and two-qudit entangled state are also considered, respectively. In these schemes the required resources are single-particle projective measurement, appropriate local unitary operation, auxiliary particle, and high-dimensional C-NOT operation. It is shown that the entanglement resource and classical communication cost are both greatly reduced in our schemes.
This paper proposes a scheme for probabilistic joint remote preparation of an arbitrary high-dimensional equatorial quantum state by using high-dimensional single-particle orthogonal projective measurement and appropriate unitary operation. As a special case, a scheme of joint remote preparation of a single-qutrit equatorial state is presented in detail. The scheme is also generalized to the multi-party high-dimensional case. It shows that, only if when all the senders collaborate with each other, the receiver can reconstruct the original state with a certain probability.
The quantum equatorial state, a special kind of quantum state, has attracted much attention because of its potential for applications in quantum information processing. The remote preparations of arbitrary two-qudit, three-qudit equatorial and m-qudit equatorial states have been studied via different entangle quantum channels. In this paper, we propose two protocols for the controlled joint remote preparation of an arbitrary m-qudit equatorial state with a pure entangled quantum channel. The first is for the controlled joint remote preparation of the m-qudit equatorial state by using m multiparticle GHZ-class states as the quantum channel, and the second is for the controlled joint remote preparation of the m-qudit equatorial state via a multiparticle entangled state. All senders share information about the prepared state and perform m-particle projective measurements on their entangled particles according to their information about the prepared state. All controllers perform generalized X-basis measurements on their entangled particles. If a receiver cooperates with all the senders and controllers, he can prepare the original state probabilistically by performing unitary operations on his entangled particles and an auxiliary qubit. This protocol is more convenient for applications because it only requires nonmaximal entanglement for the controlled joint remote preparation of an arbitrary m-qudit equatorial state.
In this paper, we proposed a protocol which can produce a perfect copy of an unknown bipartite three-dimension equatorial entangled state with assistance from a state preparer. In this protocol, the maximally entangled and non-maximally entangled two-qutrit states are used as the quantum channels, respectively. The first stage of the protocol requires the usual teleportation. In the second stage of the protocol, with the assistance of the preparer, the perfect copy of an original unknown state can be produced.