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Chinese Physics B

Controlled remote implementation of quantum operations with high-dimensional systems

You-Bang Zhan, Xiaowei Li, Peng-Cheng Ma, Jin Shi

Published Apr 1, 2013• 8 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/22/4/040306

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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.
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 propose a protocol of remote implementations of quantum operations by hybridizing bidirectional quantum-state teleportation (BQST) [Huelga et al., Phys. Rev. A 63, 042303 (2001)] and the Wang protocol [Wang, Phys. Rev. A 74, 032317 (2006)]. The protocol is available for remote implementations of quantum operations in the restricted sets specified in the paper. We also give a proof of the protocol and point out its optimization. As an extension, this hybrid protocol can be reduced to the BQST and Wang protocols.
Abstract By blending the ideas of controlled teleportation, bidirectional teleportation and remote implementation of quantum operations, we investigate the bidirectional transmission of quantum operations under the control of one supervisor. Firstly, we provide a method for generating a class of multi-particle entangled states, including five-particle and seven-particle entangled states, using a nine-particle entangled state as an example. Then using our constructed five-particle entangled state as a quantum channel, we propose a new controlled bidirectional protocol for remotely implementing partially known quantum operations (PUQOs for short) of one qubit within the two restricted sets satisfying specific conditions. Subsequently, exploiting a nine-particle entangled state as the quantum channel, we extend it to the case of two-qubit quantum operations which come from eight restricted sets. Replacing two PUQO of two qubits by a PUQO of one qubit and a PUQO of two qubits, we put forward another new asymmetric controlled bidirectional protocol for remotely implementing PKQOs via a seven-particle entangled state as the quantum channel. In these protocols, by using universal recovered operations performed by the receivers, the senders can simultaneously exchange their PUQOs as long as the controller collaborates, where each PUQO acts on the corresponding unknown state owned by the remote recipient.
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 the generalized version of Wang's protocol[A.M.Wang, Phys.Rev.A 74,032317 (2006)] for the remote implementation(sometimes referred to as quantum remote control) of partially unknown quantum operations. The protocol only requires no more than half of the entanglements used in Bidirectional Quantum State Teleportation. We also propose a protocol for another form of quantum remote control. It can remotely implement a unitary operation which is a combination of the projective representations of a group. Moreover, we prove that the Schmidt rank of the entanglements cannot not be less than the number of controlled parameters of the operations, which for the first time gives a lower bound on entanglement costs in remote implementation of quantum operations.
Abstract In this paper, we developed three protocols for the execution of the same tasks between two parties which are implementation of hidden and partially unknown quantum operators. These three protocols are respectively hierarchically controlled, controlled without hierarchy and without any controller. Our finding is that they require entangled resources with monotonically less number of involved qubits. Particularly when there is no controller, the requirement is only of one 3-qubit GHZ state for the implementation of our task.