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Advanced Quantum Technologies

Remote Implementation of Particular Subsets of Operations in two Degrees of Freedom

Mei-Yu Wang, Jiashuai Cao, B. Di

Published Dec 30, 2024• 2 citations
Publisher

Abstract

Abstract Hyperentanglement of photon systems is a fascinating resource in long‐distance quantum information processing and communication for its improvement to the channel capacity. Remote implementation of quantum operation (RIO) using a hyperentangled state has attracted much attention for its critical role in many quantum applications. In this study, a protocol for the remote implementation of particular subsets of operations exploiting a pair of photons hyperentangled in their polarization and time‐bin degrees of freedom (DOFs) is presented. The core of this scheme is to construct polarization and time‐bin parity‐check quantum nondemolition detectors (QNDs), which mainly rely on the effective cross‐Kerr nonlinear interaction and X homodyne measurements. The efficiency of the scheme is calculated in terms of bits of transmission and consumption. Compared with the RIO using the polarization‐spatial‐mode hyperentangled state, the present scheme saves resources since there is no requirement for two paths for each photon. Further, given some applicable experimental parameters, the fidelity due to the effect of decoherence in the circuits is analyzed, and the result demonstrates a high fidelity in the presence of photon dissipation. Since the time‐bin DOF is more robust over a channel, especially from space to earth, this RIO protocol presents a promising approach for building a global quantum‐communication network.

DOI
10.1002/qute.202400583

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Abstract Hyperentanglement of photon systems is a fascinating resource in long‐distance quantum information processing and communication for its improvement to the channel capacity. Remote implementation of quantum operation (RIO) using a hyperentangled state has attracted much attention for its critical role in many quantum applications. In this study, a protocol for the remote implementation of particular subsets of operations exploiting a pair of photons hyperentangled in their polarization and time‐bin degrees of freedom (DOFs) is presented. The core of this scheme is to construct polarization and time‐bin parity‐check quantum nondemolition detectors (QNDs), which mainly rely on the effective cross‐Kerr nonlinear interaction and X homodyne measurements. The efficiency of the scheme is calculated in terms of bits of transmission and consumption. Compared with the RIO using the polarization‐spatial‐mode hyperentangled state, the present scheme saves resources since there is no requirement for two paths for each photon. Further, given some applicable experimental parameters, the fidelity due to the effect of decoherence in the circuits is analyzed, and the result demonstrates a high fidelity in the presence of photon dissipation. Since the time‐bin DOF is more robust over a channel, especially from space to earth, this RIO protocol presents a promising approach for building a global quantum‐communication 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.
We present two hyperentangled concentration schemes for two-photon systems in a partially hyperentangled Bell state that is simultaneously entangled in polarization, spatial mode and time-bin degrees of freedom (DOFs). The first scheme extracts a maximally hyperentangled Bell state using cross-Kerr nonlinearity, which is discussed in two cases of unknown and known coefficients. We construct quantum nondemolition detectors based on cross-Kerr nonlinearities to implement the polarization and spatial parity check. In this scheme, we only require a small phase shift, as long as it can be distinguished from zero. The second scheme is used to concentrate an initial partially hyperentangled state with only linear optical elements, where coefficients of the initial state are known. Both of the two schemes are feasible with the current experimental technology. Moreover, hyperentanglement DOFs can largely improve the channel capacity of long-distance quantum communication. All of these make our schemes more practical and useful in quantum communication.
Abstract We present two deterministic hyperentangled state analysis protocols for photons entangled in polarization, spatial-mode and time-bin degrees of freedom (DOFs). The first protocol is a hyperentangled Bell state analyzer, and the second is a hyperentangled Greenberger–Horne–Zeilinger (GHZ) state analyzer for three photons. In the first scheme, we construct a polarization parity-check quantum nondemolition detector (P-QND) and a spatial-mode parity-check quantum nondemolition detector (S-QND) based on cross-Kerr nonlinearities. With these P-QND and S-QND, we design the setup of Bell state analyzer in polarization and spatial-mode DOFs. While time-bin entanglement is discriminated with the help of the polarization entanglement. We generalize the idea to analyze the three-photon hyperentangled GHZ states. In each scheme, a set of mutually orthogonal hyperentangled basis states are completely discriminated via three steps. These two state analysis schemes are expected to provide practical applications for high-capacity and long-distance quantum communication.
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.
Preparing quantum state remotely plays an important role in quantum communication network. Most of the previous protocols for parallel preparation quantum state remotely only consider parallel remote preparation of arbitrary single-qubit states. In this paper, we propose a protocol for parallel remote preparation of two-qubit hybrid states with a two-photon hyperentangled state. The arbitrary two-qubit hybrid states encoded in spatial-mode, frequency, polarization and time-bin degrees of freedom(DOFs) can be remotely prepared via hyperentangled state and optical elements. Moreover, we discuss parallel remote preparation of two-qubit hybrid states via partially hyperentangled state. The protocol for parallel remote preparation of two-qubit hybrid states has the advantage of having high channel capacity for long distance quantum communication by using hyperentangled state simultaneously entangled in spatial-mode, frequency, polarization and time-bin DOFs as the quantum channel.
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.