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Controlled Remote State Preparation via General Pure Three-Qubit State

Yuebo Zha, Zhihua Zhang, Yulin Huang, Jianyu Yang

Published Jul 17, 2015• 1 citation
Publisher

Abstract

The protocols for controlled remote state preparation of a single qubit and a general two-qubit state are presented in this paper. The general pure three-qubit states are chosen as shared quantum channel, which are not Local operations and classical communication (LOCC) equivalent to the mostly used GHz state. This is the first time that general pure three-qubit states have been introduced to complete remote state preparation. The probability of successful preparation is presented. Moreover, in some special cases, the successful probability could reach a unit value.

DOI
10.3390/info6030375

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The protocols for controlled remote state preparation of a single qubit and a general two-qubit state are presented in this paper. The general pure three-qubit states are chosen as shared quantum channel, which are not Local operations and classical communication (LOCC) equivalent to the mostly used GHz state. This is the first time that general pure three-qubit states have been introduced to complete remote state preparation. The probability of successful preparation is presented. Moreover, in some special cases, the successful probability could reach a unit value.
The protocols for controlled remote state preparation of a single qubit and a general two-qubit state are presented in this paper. The general pure three-qubit states are chosen as shared quantum channel, which are not LOCC equivalent to the mostly used GHZ-state. It is the first time to introduce general pure three-qubit states to complete remote state preparation. The probability of successful preparation is presented. Moreover, in some special cases, the successful probability could reach unit.
Abstract Remote state preparation is a secure and faithful method for transmitting known quantum states by means of local operation and classical communication. Existing protocols in the general case succeed just with probabilities of less than 100%. In this paper, we design a protocol to remotely prepare the most general single-qubit state that always succeeds. To achieve unit success probability, the preparer is allowed to use additional local resources and implement adaptive measurements. Our protocol is meaningful because the most expensive resource, i.e. the quantum channel previously shared between the preparer and the receiver, remains the same as in the original protocol (Pati 2000 Phys. Rev. A 63 014302), which, however, succeeds only half the time.
We present a scheme for remotely preparing an arbitrary two-qubit pure state by using two bipartite partially entangled states as the quantum channel, the scheme is then generalized to the arbitrary three-qubit case. For the two cases of remote state preparation, we construct two different efficient projective measurement bases at sender's side and calculate the corresponding success probabilities. It is shown that remote preparation of the two-qubit or three-qubit state can be probabilistically achieved with unity fidelity. Moreover, for some special ensembles of the initial states, we find that the success probability of preparation can be increased to four times for two-qubit states and eight times for three-qubit states, and is equal to one in the case of the maximal entanglement resources.
A scheme is proposed for remotely preparing a two-qubit state by using four-qubit cluster state as the quantum channel.In the scheme,the success probability of preparation and classical communication cost are calculated.In general,Bob can successfully prepare the target state with the probability 1/4 and consume only 1/4 bits classical communication.However,if the state belongs to six special situations,the success probability of preparation can reach 1/2 or even 1 after consuming some extra bits.
A scheme is proposed for remotely preparing a class of three-particle GHZ states by using a Bell state and a three-qubit GHZ state as the quantum channel. In the scheme, a two-qubit collective state measurement is performed and the necessary classical communication cost is 0.25 cbit on average. In general, the target state can be successfully prepared with the probability 1/4. However, if the state belongs to some special classes, the preparation success probability can reach 0.5 or even 1 after consuming a little additional classical resource. Comparing with the recent scheme [Opt. Commun.281, 871 (2008)], the present scheme has some advantages, e.g., the simpler quantum joint measurement and the less classical resource consumption.