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arXiv:quant-ph/0510209 · Physical Review A

Remote implementations of partially unknown quantum operations of multiqubits

An Min Wang

Published Sep 15, 2006• 68 citations
arXivHTMLPDF

Abstract

We propose and prove the protocol of remote implementations of partially unknown quantum operations of multiqubits belonging to the restricted sets. Moreover, we obtain the general and explicit forms of restricted sets and present evidence of their uniqueness and optimization. In addition, our protocol has universal recovery operations that can enhance the power of remote implementations of quantum operations.

DOI
10.1103/physreva.74.032317

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We propose and prove the protocol of remote implementations of partially unknown quantum operations of multiqubits belonging to the restricted sets. Moreover, we obtain the general and explicit forms of restricted sets and present evidence of their uniqueness and optimization. In addition, our protocol has universal recovery operations that can enhance the power of remote implementations of quantum operations.
Abstract Our concern is to investigate controlled remote implementation of partially unknown operations with multiple layers. We first propose a scheme to realize the remote implementation of single-qubit operations belonging to the restricted sets. Then, the proposed scheme is extended to the case of single-qudit operations. As long as the controller and the higher-layer senders consent, the receiver can restore the desired state remotely operated by the sender. It is worth mentioning that the recovery operation is deduced by general formulas which clearly reveal the relationship with the measurement outcomes. For the sake of clarity, two specific examples with two levels are given respectively. In addition, we discuss the influence of amplitude-damping noise and utilize weak measurement and measurement reversal to effectively resist noise.
We propose and prove protocols of combined and controlled remote implementations of partially unknown quantum operations belonging to the restricted sets [A. M. Wang, Phys. Rev. A 74, 032317 (2006)] using Greenberger-Horne-Zeilinger (GHZ) states. We present the protocols in detail in the cases of one qubit, with two senders and with one controller, respectively. Then we study the variations of protocols with many senders, or with many controllers, or with both many senders and controllers using a multipartite GHZ state. Furthermore, we extend these protocols to the cases of multiqubits. Because our protocols have to request that the senders work together and transfer the information in turn or receive the repertoire of extra supercontrollers, or/and the controller(s) open the quantum channel and distribute the passwords in different ways, they definitely have the strong security in remote quantum information processing and communications. Moreover, the combined protocol with many senders is helpful to arrive at the power of remote implementations of quantum operations to the utmost extent in theory, since the different senders may have different operational resources and different operational rights in practice, and the controlled protocol with many controllers is able to enhance security and increase applications of remote implementations of quantum operations in engineering, since it has some common features in a controlled process.
Abstract Two protocols are proposed for two closely linked but different variants of remote implementation of quantum operators of specific forms The first protocol is designed for the remote implementation of the single qubit hidden quantum operator, whereas the second one is designed for the remote implementation of the partially unknown single qubit quantum operator. In both cases two-qubit maximally entangled state, which is entangled in the spatial degree of freedom is used. The quantum resources used here are optimal and easy to realize and maintain in comparison to the multi-partite or multi-mode entangled states used in earlier works. The impact of photon loss due to interaction with the environment is analyzed for both the schemes. The proposed protocols are also generalized to their controlled, bidirectional, cyclic, controlled cyclic, and controlled bidirectional versions and it is shown that either Bell state alone or products of Bell states will be sufficient to perform these tasks with some additional classical communications in the controlled cases only. This is in sharp contrast to the earlier proposals that require large entangled states. In addition, it’s noted that remote implementation of hidden or partially unknown operators involving multiple controllers and/or multiple players who jointly apply the desired operator(s) would require quantum channels more complex than the Bell states and their products. Explicit forms of such quantum channels are also provided.
Abstract In this work, we present two schemes for the bidirectional controlled remote implementation of quantum operations. Firstly, the bidirectional controlled teleportation of two arbitrary unitary operations is considered. Then, the scheme for bidirectional controlled remote implementation of partially unknown operations belong to some restricted sets is proposed. In these schemes, two users are not only senders but also receivers. It is shown that, in these schemes, only if the two senders and controller collaborate with each other, the bidirectional controlled remote implementation of quantum operations can be completed successfully.
We present a protocol for the hierarchical controlled joint remote implementation of the partially unknown operations of m qudits belonging to some restricted sets by using m multiparticle high-dimensional entangled states as the quantum channel. All the senders share the information of the partially unknown operations and cooperate with each other to implement the partially unknown operations on the remote receiver's quantum system. The receivers are hierarchized in accordance with their abilities to reconstruct the desired state. The agents in the upper grade need only cooperate with one of the lower-grade agents, and the agents in the lower grade need the cooperation of all the other agents. The protocol has the advantage of having high channel capacity by using a high-dimensional entangle state as the quantum channel for the hierarchial controlled joint remote implementation of partially unknown quantum operations of m qudits.
We present two protocols for the controlled remote implementation of quantum operations between three-party high-dimensional systems. Firstly, the controlled teleportation of an arbitrary unitary operation by bidirectional quantum state teleportaion (BQST) with high-dimensional systems is considered. Then, instead of using the BQST method, a protocol for controlled remote implementation of partially unknown operations belonging to some restricted sets in high-dimensional systems is proposed. It is shown that, in these protocols, if and only if the controller would like to help the sender with the remote operations, the controlled remote implementation of quantum operations for high-dimensional systems can be completed.