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International Journal of Quantum Information

PROBABILISTIC MULTIPARTY-CONTROLLED REMOTE PREPARATION OF AN ARBITRARY m-QUDIT STATE VIA POSITIVE OPERATOR-VALUED MEASUREMENT

Li Zhao, Ping Zhou

Published Aug 1, 2012• 16 citations
Publisher

Abstract

We present a scheme for multiparty-controlled remote preparation of an arbitrary m-qudit (d-dimensional quantum system) state via positive operator-valued measurement (POVM) by using nonmaximally entangled states as the quantum channel, not resorting to auxiliary qubits. The sender performs an optimal POVM measurement on her m particles with measurement operators that depend on the original state, the controllers perform generalized X-basis measurement Xdand the receiver can prepare the original state if he cooperates with all the controllers and the sender. The scheme has the advantage of having high success probability for remote preparing an arbitrary m-qudit state and more convenient than others in a practical application. Moreover, it discusses the relationship between the probability that the receiver obtains the originally state and the coefficients of the entangled states.

DOI
10.1142/s0219749912500621

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We present a scheme for multiparty-controlled remote preparation of an arbitrary m-qudit (d-dimensional quantum system) state via positive operator-valued measurement (POVM) by using nonmaximally entangled states as the quantum channel, not resorting to auxiliary qubits. The sender performs an optimal POVM measurement on her m particles with measurement operators that depend on the original state, the controllers perform generalized X-basis measurement Xdand the receiver can prepare the original state if he cooperates with all the controllers and the sender. The scheme has the advantage of having high success probability for remote preparing an arbitrary m-qudit state and more convenient than others in a practical application. Moreover, it discusses the relationship between the probability that the receiver obtains the originally state and the coefficients of the entangled states.
We present a general scheme for multiparty joint remote preparation of an arbitrary m -qudit state with a pure entangled quantum channel via positive operator-valued measurement (POVM). The n senders share the information of the prepared state. The first sender performs POVM on his particles according to his knowledge of the original state, the other n − 1 senders perform m -particle projective measurement and the receiver can probabilistically reconstruct the original state by performing unitary operations on his particles according to the senders' measurement results. The scheme has the advantage of having high success probability for multiparty joint remote preparation of an arbitrary m -qudit state via pure entangled quantum states. Moreover, it discusses the relationship between the coefficients of the pure entangled states and the success probability.
We present a scheme for symmetric controlled remote preparation of an arbitrary 2-qudit state form a sender to either of the two receivers via positive operator-valued measurement and pure entangled two-particle states. The first sender transforms the quantum channel shared by all the agents via POVM according to her knowledge of prepared state. All the senders perform single- or two-particle projective measurements on their entangled particles and the receiver can probabilisticaly reconstruct the original state on her entangled particles via unitary transformation and auxiliary qubit. The scheme is optimal as the probability which the receiver prepares the original state equals to the entanglement of the quantum channel. Moreover, it is more convenience in application than others as it requires only two-particle entanglements for preparing an arbitrary two-qudit state.
A scheme for remotely preparing an arbitrary two-particle pure state is proposed by employing bipartite nonmaximally entangled states as quantum channels. During the preparation, two auxiliary particles and an optimal positive operator-valued measurement are introduced. The preparation of two-particle pure states can be remotely realized with certain success probability (SP). And the SP of our scheme is exactly worked out. It turns out that the SP depends inherently on the quantum channels employed beforehand. Furthermore, we find that, as far as two special ensembles of two-particle states are concerned, i.e. real and equatorial-like, the SP can be enhanced to quadruple.
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.
By means of the method of the positive operator-valued measure, two schemes to remotely prepare an arbitrary two-particle entangled state were presented. The first scheme uses a one-dimensional four-particle non-maximally entangled cluster state while the second one uses two partially entangled two-particle states as the quantum channel. For both schemes, if Alice performs two-particle projective measurements and Bob adopts positive operator-valued measure, the remote state preparation can be successfully realized with certain probability. The success probability of the remote state preparation and classical communication cost are calculated. It is shown that Bob can obtain the unknown state with probability 1/4 for maximally entangled state. However, for four kinds of special states, the success probability of preparation can be enhanced to unity.
We propose two protocols for joint, multi-party remote preparation of qudit states by using a d-level six-qudit Cluster state as the quantum channel. The first protocol is used for the joint remote preparation of an arbitrary two-qudit state via the d-level six-qudit Cluster state. The second is used for bi-directional joint remote preparation of an arbitrary single-qudit state via a d-level six-qudit Cluster state. All senders share information about the prepared state. The first sender applies Positive Operator-Valued Measurement (POVM) on her entangled particles in accordance with her information about the prepared state, while the second sender performs projective measurements in accordance with the information about the prepared state and the first sender’s measurement results. The receiver can prepare the original state by performing a corresponding unitary operation according to the measurement results from all the senders. These two protocols have the advantage of being able to provide a high channel capacity by using a d-level Cluster state as the quantum channel.