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arXiv:quant-ph/0603036 · Physical Review A

Remote preparation of a qudit using maximally entangled states of qubits

Chang‐shui Yu, He‐Shan Song, Yahong Wang

Published Feb 23, 2006• 99 citations
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Abstract

Known quantum pure states of a qudit can be remotely prepared onto a group of particles of qubits exactly or probabilistically with the aid of two-level Einstein--Podolsky--Rosen states. We present a protocol for such kind of remote state preparation. We are mainly focused on the remote preparation of the ensembles of equatorial states and those of states in real Hilbert space. In particular, a kind of states of qudits in real Hilbert space have been shown to be remotely prepared in faith without the limitation of the input space dimension.

DOI
10.1103/physreva.73.022340

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Known quantum pure states of a qudit can be remotely prepared onto a group of particles of qubits exactly or probabilistically with the aid of two-level Einstein--Podolsky--Rosen states. We present a protocol for such kind of remote state preparation. We are mainly focused on the remote preparation of the ensembles of equatorial states and those of states in real Hilbert space. In particular, a kind of states of qudits in real Hilbert space have been shown to be remotely prepared in faith without the limitation of the input space dimension.
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 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.
We propose several schemes for the joint remote preparation of four-qubit cluster-type states with real coefficients and complex coefficients by using six Einstein–Podolsky–Rosen (EPR) pairs and two six-qubit entangled states as quantum channels respectively. In these schemes, two senders share the original state which they wish to help the receiver to remotely prepare. It is shown that, only if two senders collaborate with each other, and perform four-qubit projective measurements on their own qubits respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations.