The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this potential, efficient schemes for entangling operations such as the high-dimensional generalization of a linear optics Bell measurement will be required. We show how an efficient high-dimensional entangled state analyzer can be implemented with a linear optics interferometer and auxiliary photonic states. The degree of entanglement of the auxiliary state is much less than in previous protocols as quantified by an exponentially smaller Schmidt rank. In addition, the auxiliary state only occupies a single spatial mode, allowing it to be generated deterministically from a single quantum emitter coupled to a small qubit register. The reduced complexity of the auxiliary states results in a high robustness to imperfections and we show that auxiliary states with fidelities above 0.9 for qudit dimensions 4 can be generated in the presence of qubit error rates on the order of 10%. This paves the way for experimental demonstrations with current hardware.
The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this potential, efficient schemes for entangling operations such as the high-dimensional generalization of a linear optics Bell measurement will be required. We show how an efficient high-dimensional entangled state analyzer can be implemented with a linear optics interferometer and auxiliary photonic states. The degree of entanglement of the auxiliary state is much less than in previous protocols as quantified by an exponentially smaller Schmidt rank. In addition, the auxiliary state only occupies a single spatial mode, allowing it to be generated deterministically from a single quantum emitter coupled to a small qubit register. The reduced complexity of the auxiliary states results in a high robustness to imperfections and we show that auxiliary states with fidelities above 0.9 for qudit dimensions 4 can be generated in the presence of qubit error rates on the order of 10%. This paves the way for experimental demonstrations with current hardware.
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 N-qudit (N>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 X gates and Z 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.
Quantum gates are the essential block for quantum computer. High-dimensional quantum gates exhibit remarkable advantages over their two-dimensional counterparts for some quantum information processing tasks. Here we present a family of entanglement-based optical controlled-SWAP gates on C2⊗Cd⊗Cd. With the hybrid encoding, we encode the control qubits and target qudits in photonic polarization and spatial degrees of freedom, respectively. The circuit is constructed using only (2+3d) (d≥2) linear optics, beating an earlier result of 14 linear optics with d=2. The circuit depth 5 is much lower than an earlier result of 11 with d=2. Besides, the fidelity of the presented circuit can reach 99.4\%, and it is higher than the previous counterpart with d=2. Our scheme are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Moreover, our approach allows d>2.
In quantum communication and fusion-based quantum computation, photonic Bell measurements are fundamentally limited when only passive linear optics is employed. While for qubits, some Bell states can be unambiguously identified with static beam splitters and no extra photons or entanglement, additional auxiliary photons or at least additional auxiliary degrees of freedom with a certain level of additional entanglement are needed to approach or attain a complete, deterministic Bell measurement. Here, we prove an exact resource threshold when the same two photons carry system qudits of dimension d and a fixed auxiliary entangled state Φ, possibly distributed over several additional degrees of freedom, with total Schmidt rank rΦ. We show that a single conclusive Bell-label functional can occur for rΦ⩾⌈d/2⌉, but deterministic discrimination of all d2 Bell-state labels requires rΦ⩾d. A maximally entangled rank-d auxiliary state achieves the bound by local Bell-basis sorting between each photon's system and auxiliary degrees of freedom. Thus, the auxiliary Schmidt rank is a certified resource for ancilla-photon-free, embedded photonic Bell measurements.
Compared with traditional two-dimensional qubits, higher-dimensional qubits offer a larger state space for storing and processing information, which can manifest stronger non-classical correlations, simplify circuit complexity, reduce computational resources, and enhance loss tolerance in photon-based quantum information processing. To harness the potential, essential research on preparing qudit-based high-dimensional entangled states is necessary. In the paper, we propose the preparation procedure of arbitrary four-dimensional two-qudit entanglement and three-qudit entanglement for photon systems implemented with error-heralded quantum devices and controlled-not gates. Moreover, as the practical errors that grow out of defective photon scattering, i.e., coupling strength restriction of the quantum-dot-cavity system and cavity leakage imperfection, can be turned into the response of the single-photon detectors, the generation of arbitrary high-dimensional entanglement appears in an error-heralded way, and their fidelities are robust, enhancing experimental accessibility.
Implementing quantum logic gates with linear optical elements is a key approach in photon-based quantum information processing (QIP) due to its operational convenience and experimental flexibility. The adoption of high-dimensional (H-D) quantum computing with qudit encoding over conventional 2-D qubit encoding offers higher information encoding capability. In this paper, we present a linear-optics-based two-qudit 4×4-D (16-D) controlled-SUM (CSUM) gate for photon systems, where the polarization degrees of freedom (DoFs) of two photons encode the 4-D control qudit and the polarization and spatial DoFs of another single photon encode the 4-D target qudit. The 16-D CSUM gate demonstrates an efficiency of 1/243 and a theoretical average fidelity of 0.98395. Additionally, the H-D CSUM gate neither requires ancillary photons and pre-shared entanglement nor presents complex quantum circuits, thus significantly reducing the experimental overhead and enhancing its feasibility with current technology.
In this paper, we propose a linear-optical quantum computation scheme that starts from high-dimensionally entangled qudits but performs quantum computation on qubits defined in their subspaces. This approach enables us to increase the success probability of linear-optical fusions from 50% to 1−1/d for qudits of dimension d without relying on existing approaches using ancilla photons and quantum codes. In particular, we show that a 2D cluster state of qubits can be generated from 5-qudit 1D cluster states using pairwise fusion gates while preserving their boosted success probability. We numerically demonstrate that this approach can improve the loss tolerance of a percolation-based scheme while keeping the photon number per resource state constant.