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arXiv:2210.14674 · Annalen der Physik

Controlled Remote Implementation of Operations via Graph States

Xinyu Qiu, Lin Chen

Published Nov 14, 2023• 5 citations
arXivHTMLPDF

Abstract

Abstract Protocols are proposed for controlled remote implementation of operations here. Sharing a ‐partite graph state, 2N participants collaborate to prepare the stator and realize the operation on N unknown states for distributed systems , only with the permission of a controller. The control power analysis shows that without the controller's permission, eight specified operations can be implemented with the success rate of 50%, other operations can be realized with the success rate of 25%, and thus the control power is reliable. All the implementation requirements of this protocol can be satisfied by means of local operations and classical communications, and the experimental feasibility is presented according to current techniques. The entanglement requirement of this protocol is characterized in terms of geometric measure of entanglement. It turns out to be economic to realize the control function from the perspective of entanglement cost.

DOI
10.1002/andp.202300320

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Abstract Protocols are proposed for controlled remote implementation of operations here. Sharing a ‐partite graph state, 2N participants collaborate to prepare the stator and realize the operation on N unknown states for distributed systems , only with the permission of a controller. The control power analysis shows that without the controller's permission, eight specified operations can be implemented with the success rate of 50%, other operations can be realized with the success rate of 25%, and thus the control power is reliable. All the implementation requirements of this protocol can be satisfied by means of local operations and classical communications, and the experimental feasibility is presented according to current techniques. The entanglement requirement of this protocol is characterized in terms of geometric measure of entanglement. It turns out to be economic to realize the control function from the perspective of entanglement cost.
Quantum entanglement is essential for the realization of distributed computing and has been implemented in various types of two-level systems. However, high-dimensional quantum protocols are rarely investigated both theoretically and experimentally, despite the remarkable advantages that high-dimensional quantum systems exhibit over two-level systems for certain quantum information and computing tasks. Here, we propose asymmetric protocols that utilize different dimensional systems to prepare the stator and achieve remote state operations with the assistance of shared N -partite graph states. Our protocols demonstrate convincing control power and security, with all implementations achievable through local operations and classical communications. The experimental realization of high-dimensional quantum systems and operations is presented using current technology. Our work contributes towards achieving arbitrary high-dimensional quantum protocols and paves the way for implementing high-dimensional quantum communication and computation.
We present new controlled remote implementation of operations (CRIO) protocols based on graph states, which allow two controllers to jointly govern remote quantum operation exp [𝑖𝛼𝜎n]. Two protocols, CRIO in quartet and six-partite, are introduced in this paper. The first protocol contains two controllers, a sender and a receiver, the second protocol allows two pairs of sender and receiver to implement the remote operations only with the permission of both controllers. Our approach improves security control at the cost of requiring more entanglement resources than previous methods. All the implementation can be achieved by using local operation and classical communication (LOCC). These protocols contribute to multi-controller quantum networks and need future optimizations enhance the experimental feasibility.
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.
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 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.
Quantum remote control, also known as quantum remote implementation of an operator (QRIO), enables the remote manipulation of an arbitrary quantum state by implementing a desired quantum operation at a distant location. Significant progress has recently been made in developing QRIO protocols and their variants. Most existing schemes employ hyperentangled states where entanglement is shared across multiple degrees of freedom (DOFs). However, these protocols typically exploit only one degree of freedom at a time. In this work, we propose a QRIO protocol that simultaneously utilizes the polarization and spatial DOFs of a two-qubit hyperentangled state to remotely implement an arbitrary hybrid operator on an unknown single-photon two-qubit hyperstate. The shared hyperentangled resource is realized using the polarization and spatial modes of photons, while the protocol is constructed using linear optical elements and cross-Kerr nonlinear interactions to facilitate effective photon-photon coupling. Furthermore, the effects of measurement errors arising from finite coherent state distinguishability and coherent state dissipation are analyzed and the corresponding success probability of the protocol is evaluated. The results demonstrate that an appropriate choice of the cross-Kerr phase shift and coherent state amplitude significantly enhances the protocol performance, making the proposed scheme a promising candidate for hybrid quantum communication and distributed quantum information processing.