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Laser Physics

Deterministic high-dimensional quantum remote implementation via hybrid photonic encoding

Qi-Qi Dong, Junqiang Wang

Published Aug 1, 2025• 1 citation
Publisher

Abstract

Abstract Remote implementation of high-dimensional quantum operation is pivotal for advancing quantum communication and distributed computing. Here, we propose a deterministic protocol capable of performing arbitrary four-dimensional unitary operations between two spatially separated nodes. The scheme utilizes hybrid encoding in both polarization and spatial degrees of freedom, which not only conserves quantum resources but also leverages the scalability of high-dimensional photonic systems. A key feature of the protocol is the use of weak cross-Kerr nonlinearities combined with X -quadrature homodyne detection. This design significantly reduces the reliance on strong nonlinear interactions and enhances robustness against photon loss. By performing classical feed-forward operations conditioned on coherent-state measurement outcomes, our approach ensures deterministic execution and high operational fidelity. Importantly, the protocol avoids the need for complex ancillary entanglement by relying solely on linear optics and simplified measurements. Due to the use of mature optical components and a loss-resilient architecture, numerical simulations under realistic experimental conditions indicate a high success probability (≈1) of this scheme. These advantages highlight the practicality and resource efficiency of our method, making it well-suited for the implementation of high-dimensional quantum communication protocols with current photonic technologies.

DOI
10.1088/1555-6611/adf837

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Abstract Remote implementation of high-dimensional quantum operation is pivotal for advancing quantum communication and distributed computing. Here, we propose a deterministic protocol capable of performing arbitrary four-dimensional unitary operations between two spatially separated nodes. The scheme utilizes hybrid encoding in both polarization and spatial degrees of freedom, which not only conserves quantum resources but also leverages the scalability of high-dimensional photonic systems. A key feature of the protocol is the use of weak cross-Kerr nonlinearities combined with X -quadrature homodyne detection. This design significantly reduces the reliance on strong nonlinear interactions and enhances robustness against photon loss. By performing classical feed-forward operations conditioned on coherent-state measurement outcomes, our approach ensures deterministic execution and high operational fidelity. Importantly, the protocol avoids the need for complex ancillary entanglement by relying solely on linear optics and simplified measurements. Due to the use of mature optical components and a loss-resilient architecture, numerical simulations under realistic experimental conditions indicate a high success probability (≈1) of this scheme. These advantages highlight the practicality and resource efficiency of our method, making it well-suited for the implementation of high-dimensional quantum communication protocols with current photonic technologies.
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.
The generation of a high-dimensional quantum entangled state provides a crucial resource for achieving more complex and diverse quantum information processing tasks. In this paper, we present two deterministic protocols designed for the generation of a four-dimensional two-qudit Bell state and three-qudit Greenberger-Horne-Zeilinger (GHZ) state assisted by cross-Kerr nonlinearity, where the four-dimensional qudit is encoded in the hybrid polarization-spatial state of the single photon to conserve quantum resources and alleviate environmental noise. The proposed protocols for generating a four-dimensional two-qudit Bell state and three-qudit GHZ state are circuit concise, high success, robust fidelity, noise resistant, and resource saving. Moreover, the four-dimensional NNN-qudit (N>3N>3N>3) GHZ states can be generated with the help of the $N\ensuremath{-}1$ generating devices of the four-dimensional Bell state. Consequently, its efficiency and fidelity decay exponentially by a factor of $N\ensuremath{-}1$. Further, the arbitrary high-dimensional qudit-encoded entangled states can be achieved with linear-optics four-dimensional single-qudit XXX gates and ZZZ gates. These protocols offer a reference for further advancements in high-dimensional state generation technology and providing insights for the practical implementations of metrological enhancement, quantum simulation, high-dimensional quantum computation, and quantum error correction.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to the relatively easier manipulation and realization. We present efficient schemes to implement controlled-NOT (CNOT) gate and controlled-swap (Fredkin) gate by solely using linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd-level), respectively. Based on the hybrid encoding, CNOT and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a CNOT gate has been reduced to one polarization beam splitter (PBS), while only ddd PBSs are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to one and dimension-independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7\% under realistic conditions, which is higher than the previous schemes.
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.
Quantum entanglement between pairs of remote quantum memories (QMs) is a prerequisite for realizing many applications in quantum networks. Here, we present a heralded protocol for the parallel creation of quantum entanglement among multiple pairs of QMs placed in spatially separated nodes, where each QM, encoding a stationary qubit, couples to an optical cavity and deterministically interacts with single photons. Our protocol utilizes an entangled photon pair encoded in the high-dimensional time-bin degree of freedom to simultaneously entangle multiple QM pairs, and is efficient in terms of reducing the time consumption and photon loss during transmission. Furthermore, our approach can be extended to simultaneously support spatial-temporal multiplexing, as its success is heralded by the detection of single photons. These distinguishing features make our protocol particularly useful for long-distance quantum communication and large-scale quantum networks.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to their relatively easy manipulation and realization. We present efficient schemes to implement controlled-not (cnot) gates and controlled-swap (Fredkin) gates by using solely linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd level), respectively. On the basis of the hybrid encoding, cnot and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a cnot gate has been reduced to one polarizing beam splitter, while only ddd polarizing beam splitters are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to 1 and and are dimension independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7% under realistic conditions, which is higher than in previous schemes.