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Chinese Physics B

Probabilistic joint remote preparation of a high-dimensional equatorial quantum state

You-Bang Zhan, Qun-Yong Zhang, Shi Jin

Published Aug 1, 2010• 28 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/19/8/080310

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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.
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.
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.
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.
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.
Abstract We present two schemes for perfectly cloning an unknown single-qutrit equatorial state with assistance from two and N state preparers, respectively. In the first scheme, the sender wishes to teleport an unknown single-qutrit equatorial state from two state preparers to a remote receiver, and then to create a perfect copy of the unknown state at her location. The scheme consists of two stages. The first stage of the scheme requires the usual teleportation. In the second stage, to help the sender realize the quantum cloning, two state preparers perform single-qutrit projective measurements on their own qutrits from the sender, then the sender can acquire a perfect copy of the unknown state. It is shown that, only if the two state preparers collaborate with each other, the sender can create a copy of the unknown state by means of some appropriate unitary operations. In the second scheme, we generalized the jointly assisted cloning in the first scheme to the case of N state prepares. In the present schemes, the total probability of success for assisted cloning of a perfect copy of the unknown state can reach 1.