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Journal of Physics A Mathematical and Theoretical

Controlled remote implementation of operators via hyperentanglement

Nguyen Ba An, Bich Thi Cao

Published Apr 20, 2022• 15 citations
Publisher

Abstract

Abstract Distributed quantum computation is a good solution for salable quantum computation within a quantum network each node of which just contains reasonably a few number of qubits. Controlled implementation of operators on states of a remote node is thus necessary. In this paper we propose protocols for three kinds of tasks of controlled implementation of operators on remote photon states via one hyperentangled Greenberger–Horne–Zeilinger state assisted with cross-Kerr nonlinearities: one with general operators and photon states in spatial degree of freedom (DOF), another one also with general operators but the photon state being in polarization DOF and the third one with a limited subset of operators acting on photon state in both spatial and polarization degrees of freedom. All the protocols are deterministic and performed in two steps under quantum control in each step.

DOI
10.1088/1751-8121/ac68b2

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Abstract Distributed quantum computation is a good solution for salable quantum computation within a quantum network each node of which just contains reasonably a few number of qubits. Controlled implementation of operators on states of a remote node is thus necessary. In this paper we propose protocols for three kinds of tasks of controlled implementation of operators on remote photon states via one hyperentangled Greenberger–Horne–Zeilinger state assisted with cross-Kerr nonlinearities: one with general operators and photon states in spatial degree of freedom (DOF), another one also with general operators but the photon state being in polarization DOF and the third one with a limited subset of operators acting on photon state in both spatial and polarization degrees of freedom. All the protocols are deterministic and performed in two steps under quantum control in each step.
Abstract We propose a deterministic protocol for three distant parties to cooperate so that two parties can implement their secret unitary operators on the third party’s secret quantum state via shared quantum channel assisted by cross-Kerr nonlinearities. The operators are of general form while the state may be encoded either in spatial degree of freedom or polarization degree of freedom. The quantum channel is served by a three-photon hyperentangled state establishing the minimum of consumed photon number for this type of task. This protocol can be named joint remote implementation of operators which is necessary for distributed quantum tasks throughout a quantum network.
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.
Abstract Joint remote implementation of quantum operations (JRIO) is crucial for distributed quantum computation. We propose a probabilistic JRIO scheme using a three-photon nonmaximally hyperentangled Greenberger-Horne-Zeilinger (GHZ) state, which is simultaneously entangled in the polarization and spatial-mode degrees of freedom (DOFs), as the shared quantum resource. This JRIO protocol operates on two core principles: transferring the quantum-state information of the target qubit to the senders’ joint system via polarization-DOF entanglement and applying local operations, then executing quantum operations on the receiver’s system using entanglement in the spatial-mode DOF. The construction of the proposed scheme requires weak cross-Kerr nonlinearities, X homodyne measurements, simple linear optical elements, and common single-photon detectors. This work extends the framework of the previous JRIO protocol to the scenario of a nonmaximally hyperentangled quantum channel, enriching the theoretical family of distributed quantum operation schemes.
Implementing CNOT operation nonlocally is one of central tasks in distributed quantum computation. Most of previously protocols for implementation quantum CNOT operation only consider implement CNOT operation in one degree of freedom(DOF). In this paper, we present a scheme for nonlocal implementation of hyper-parallel CNOT operation in polarization and spatial-mode DOFs via hyperentanglement. The CNOT operations in polarization DOF and spatial-mode DOF can be remote implemented simultaneously with hyperentanglement assisited by cross-Kerr nonlinearity. Hyper-parallel nonlocal CNOT gate can enhance the quantum channel capacity for distributed quantum computation and long-distance quantum communication. We discuss the experiment feasibility for hyper-parallel nonlocal gate. It shows that the protocol for hyper-parallel nonlocal CNOT operation can be realized with current technology.
Remote implementation of quantum operation between two distant nodes is crucial for many quantum applications. Here we consider the implementation of an arbitrary single-photon operation upon a remote quantum system exploiting photon pairs simultaneously entangled in the polarization and temporal degrees of freedom, which is a fascinating resource in long-distance quantum communication with its outstanding merits. To improve the level of security for the above protocol, we also consider a controlled implementation of quantum operation scenario by adding a supervisor, which is necessary for distributed quantum computation in a quantum network. Both of the protocols can be fulfilled by bidirectional state teleportation with the aid of the effective cross-Kerr interaction. Furthermore, the simple construction circuits together with available existing optical elements and common single-photon detectors facilitate the realization of our protocols with current sufficient technologies.
Quantum information processing via hyperentanglement can improve the quantum channel capacity for long-distance quantum communication and large-scale quantum communication networks. Some important works have been presented in quantum remote state preparation with hyperentangled states. However, the protocols for quantum operation remote implementation are based on quantum systems encoded in one degree of freedom. We present a quantum operation remote implementation protocol for arbitrary single-qubit operations with two-photon hyperentangled states via cross-Kerr nonlinearities. Moreover, we discuss the scheme for parallel remote implementation of partially unknown quantum operations via two-photon hyperentangled states.