Parity-check Gate Research Articles

Compact entanglement concentration for three-electron-spin W states with error-detected parity-check gates

We present a compact entanglement concentration protocol (ECP) for unknown less-entangled three-electron-spin W states, resorting to the interaction rules between the circularly polarized photon and cavity-quantum-dot (QD) system. In the first step of our ECP, the parties utilize two less-entangled three-electron-spin systems not only to obtain one partially entangled three-electron-spin system with two unknown parameters if the odd-parity occurs with the parity-check gate (PCG) but also to get one entangled two-electron-spin system if the even-parity occurs. By exploiting the above three-electron-spin and two-electron-spin systems as the resource for the second step of our ECP, the parties can obtain a standard three-electron-spin W state if the odd parity occurs. Meanwhile, the systems in the even-parity instance can be used as the resource in the next round of our ECP. As the imperfect performances originated from the side leakage and the limited coupling strength of the cavity-QD system can be reflected by clicking the single-photon detectors, the fidelity of the PCG is unit, in principle, immune to strong coupling-strength restriction. Moreover, the success of our ECP not only is heralded by the detectors but also its efficiency further is improved by repeating the operation processes. Therefore, our ECP is useful in the quantum communication network.

Faithful and efficient hyperentanglement purification for spatial-polarization-time-bin photon system

We present a faithful and efficient hyperentanglement purification protocol (hyper-EPP) for nonlocal two-photon systems in spatial-polarization-time-bin hyperentangled Bell states. As the single-photon detectors can detect and herald the undesirable properties caused by side leakage and finite coupling strength, the parity-check gates and swap gates of our hyper-EPP in the spatial, polarization and time-bin mode degrees of freedom (DoFs) work faithfully. The qubit-flip errors in photon systems in three DoFs can be corrected effectively with the faithful parity-check gates and the photon pairs can be reused to distill high-fidelity ones by introducing the faithful swap gates, which greatly increases the efficiency of our hyper-EPP. Further, the maximal hyperentanglement can be obtained in principle by operating multiple rounds of the hyper-EPP.

High-Fidelity Photonic Three-Degree-of-Freedom Hyperparallel Controlled-Phase-Flip Gate

Encoding computing qubits in multiple degrees of freedom (DOFs) of a photonic system allows hyperparallel quantum computation to enlarge channel capacity with less quantum resource, and constructing high-fidelity hyperparallel quantum gates is always recognized as a fundamental prerequisite for hyperparallel quantum computation. Herein, we propose an approach for implementing a high-fidelity photonic hyperparallel controlled-phase-flip (CPF) gate working with polarization, spatial-mode, and frequency DOFs, through utilizing the practical interaction between the single photon and the diamond nitrogen vacancy (NV) center embedded in the cavity. Particularly, the desired output state of the gate without computation errors coming from the practical interaction is obtained, and the robust fidelity is guaranteed in the nearly realistic condition. Meanwhile, the requirement for the experimental realization of the gate is relaxed. In addition, this approach can be generalized to complete the high-fidelity photonic three-DOF hyperparallel CPFN gate and parity-check gate. These interesting features may make the present scheme have potential for applications in the hyperparallel quantum computation.

Heralded entanglement purification protocol using high-fidelity parity-check gate based on nitrogen-vacancy center in optical cavity**Project supported by the National Natural Science Foundation of China (Grants Nos. 11674033, 11474026, 11604226, and 11475021) and Science and Technology Program Foundation of the Beijing Municipal Commission of Education of China (Grant Nos. KM201710028005 and CIT&TCD201904080).

The decoherence of entangled states caused by the noisy channel is a salient problem for reducing the fidelity of quantum communication. Here we present a heralded two-photon entanglement purification protocol (EPP) using heralded high-fidelity parity-check gate (HH-PCG), which can increase the entanglement of nonlocal two-photon polarization mixed state. The HH-PCG is constructed by the input-output process of nitrogen-vacancy (NV) center in diamond embedded in a single-sided optical cavity, where the errors caused by the imperfect interaction between the NV center-cavity system and the photon can be heralded by the photon detector. As the unwanted components can be filtrated due to the heralded function, the fidelity of the EPP scheme can be enhanced considerably, which will increase the fidelity of quantum communication processing.

Hyperentanglement concentration of nonlocal two-photon six-qubit systems with linear optics

Hyperentanglement, the entangled states in the multiple degrees of freedom (DOFs) of a photon system simultaneously, has attracted much attention recently as it can increase the capacity of quantum communication largely. Here we present the first scheme for concentrating the nonlocal two-photon six-qubit systems entangled in polarization, spatial-mode, and time-bin DOFs with linear optics. We construct the parity-check gates for the quantum states of nonlocal photon systems in all the three DOFs with linear-optical elements. Fortunately, our parity-check gate for one DOF does not affect the quantum states in the other two DOFs, which makes our hyperentanglement concentration protocol (hyper-ECP) can be implemented conveniently for polarization–spatial–time-bin partially hyperentangled states. This hyper-ECP is practical as it requires only linear-optical elements, and it can be directly generalized to improve the entanglement of nonlocal multi-photon systems entangled in three DOFs in the long-distance high-capacity quantum communication.

Refined entanglement concentration for electron-spin entangled cluster states with quantum-dot spins in optical microcavities

We present a refined entanglement concentration protocol (ECP) for an arbitrary unknown less-entangled four-electron-spin cluster state by exploring the optical selection rules derived from the quantum-dot spins in one-sided optical microcavities. In our ECP, the parties obtain not only the four-electron-spin systems in the partial entanglement with two unknown parameters, but also the less-entangled two-electron-spin systems in the first step. Utilizing the above preserved systems as the resource for the second step of our ECP, the parties can obtain a standard cluster state by keeping the robust odd-parity instances with two parity-check gates. Meanwhile, the systems in the rest three instances can be used as the resource in the next round of our ECP. The success probability of our ECP is largely increased by iteration of the ECP process. Moreover, all the coefficients of our ECP are unknown for the parties without assistance of extra single electron-spin, so our ECP maybe has good applications in quantum communication network in the future.

Heralded high-efficiency quantum repeater with atomic ensembles assisted by faithful single-photon transmission.

Quantum repeater is one of the important building blocks for long distance quantum communication network. The previous quantum repeaters based on atomic ensembles and linear optical elements can only be performed with a maximal success probability of 1/2 during the entanglement creation and entanglement swapping procedures. Meanwhile, the polarization noise during the entanglement distribution process is harmful to the entangled channel created. Here we introduce a general interface between a polarized photon and an atomic ensemble trapped in a single-sided optical cavity, and with which we propose a high-efficiency quantum repeater protocol in which the robust entanglement distribution is accomplished by the stable spatial-temporal entanglement and it can in principle create the deterministic entanglement between neighboring atomic ensembles in a heralded way as a result of cavity quantum electrodynamics. Meanwhile, the simplified parity-check gate makes the entanglement swapping be completed with unity efficiency, other than 1/2 with linear optics. We detail the performance of our protocol with current experimental parameters and show its robustness to the imperfections, i.e., detuning and coupling variation, involved in the reflection process. These good features make it a useful building block in long distance quantum communication.

Systematic entanglement concentration for unknown less-entangled three-photon W states

We present a systematic entanglement concentration protocol (ECP) for an arbitrary unknown less-entangled three-photon W state, resorting to the optical property of the quantum-dot spins inside one-sided optical microcavities. In our ECP, the parties obtain not only some three-photon systems in the partially entangled with two unknown parameters when one of the parties picks up the robust odd-parity instance with the parity-check gate (PCG) on his two photons, but also some entangled two-photon systems by keeping the even-parity instance in the first step. By exploiting the above three-photon and two-photon systems with the same parameters as the resource for the second step of our ECP, the parties can obtain a standard three-photon W state by keeping the robust odd-parity instance. Meanwhile, the systems in the even-parity instance can be used as the resource in the next round of our ECP. The success probability of our ECP is largely increased by iteration of the ECP process. As it does require that all the coefficients are unknown for the parties, our ECP maybe have good applications in quantum communication network in future.

Complete Analysis of Four-Photon χ-Type Entangled State via Cross-Kerr Nonlinearity**Supported by the National Natural Science Foundation of China under Grant No. 11004258, and Fundamental Research Funds for the Central Universities Project under Grant No. CQDXWL-2012-014, the Natural Science Foundation Project of CQ CSTC 2011jjA90017

We propose an efficient method to construct an optical four-photon |χ〉 state analyzer via the cross-Kerr nonlinearity combined with linear optical elements. In this protocol, two four-qubit parity-check gates and two controlled phase gates are employed. We show that all the 16 orthogonal four-qubit |χ〉 states can be completely discriminated with our apparatus. The scheme is feasible and realizable with current technology. It may have useful potential applications in quantum information processing which based on |χ〉 state.

Parity-gate-based quantum information processing in decoherence-free subspace with nitrogen-vacancy centers

We propose a parity-check gate (PCG) for logical qubits encoded in decoherence-free subspace (DFS) by the coherent optical pulse input–output process with nitrogen-vacancy (NV) centers fixed on the surface of microtoroidal resonators (MTRs) with quantized whispering-gallery modes (WGMs). Using the proposed PCG, we achieve controlled phase flip (CPF) gate, |χ〉 state generation, and multipartite entanglement purification. The present schemes combine the advantages of the robustness of coherent pulse and the immunity to the dephasing noise of the DFS. The performances of these schemes are also analyzed, which shows that all the schemes works well in the low-Q cavity regime and are feasible under the current experimental technology.

Efficient Generation of Quantum Cluster Entangled States for Distant Diamond Nitrogen-Vacancy Centers

We present an efficient scheme for creating electronic quantum cluster entangled states associated with distant diamond nitrogen-vacancy (NV) centers coupled to microtoroidal resonators using parity-check and controlled-phase gates. These two gates are constructed by exploiting the input-output processes of single photons as a result of cavity quantum electrodynamics. Our schemes provides an efficient route to solid-state one-way quantum computation as diamond NV centers exhibit the ultralong coherent time and fast electron-spin manipulation. The time scale of the quantum cluster entangled states is a parity-check gate and a controlled-phase gate. Moreover, the prior entanglement is not required, and a higher fidelity and a higher efficiency of the quantum cluster states can be achieved, compared with other protocols.

Hybrid entanglement purification for quantum repeaters

We present an entanglement purification protocol (EPP) to reconstruct some maximally hybrid entangled states (HESs) from nonmaximally mixed HESs. We use simple linear optical elements such as a polarization beam splitter (PBS) and beam splitter (BS) to achieve this task. Meanwhile, it is shown that the parity-check gates acted by PBS and BS are enough to complete the task, and the controlled-not (cnot) gates or similar logic operations are not needed. Unlike the current EPPs, this protocol can purify not only the conventional bit-flip error and phase-flip error but also the dissipation error coming from the photon loss of the coherent state. It can also be extended to achieve the purification for multiphoton and multicoherent state HES. This protocol may be useful in current hybrid quantum repeaters.

Entanglement concentration for multi-particle partially entangled W state using nitrogen vacancy center and microtoroidal resonator system

In this paper, we present an efficient entanglement concentration protocol (ECP) for N spatially separated nitrogen-vacancy (N-V) centers coupled to microtoroidal resonators in a partially entangled W state. The robustness of W-type entanglement contrasts strongly with the Greenberger-Horne-Zeilinger (GHZ) state which is fully separable after loss of one qubit. We construct the parity-check gate by introducing an auxiliary N-V center in microcavity and a single photon. Based on the parity-check measurement and local operations, the remote parities can distill a maximally entangled W state from a partially entangled state with a certain success probability. By iterating the concentration process several times, the present ECP can obtain an optimal yield. With its robustness and scalability, the present ECP for entangled N-V center ensembles can be widely applied to quantum repeaters and long-distance quantum communications.

Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities

We present an entanglement purification protocol and an entanglement concentration protocol for electron-spin entangled states, resorting to quantum-dot spin and optical-microcavity-coupled systems. The parity-check gates (PCGs) constructed by the cavity-spin-coupling system provide a different method for the entanglement purification of electron-spin entangled states. This protocol can efficiently purify an electron ensemble in a mixed entangled state. The PCGs can also concentrate electron-spin pairs in less-entangled pure states efficiently. The proposed methods are more flexible as only single-photon detection and single-electron detection are needed.

Lossy Data Compression with Random Gates

We introduce a new protocol for a lossy data compression algorithm which is based on constraint satisfaction gates. We show that the theoretical capacity of algorithms built from standard parity-check gates converges exponentially fast to the Shannon's bound when the number of variables seen by each gate increases. We then generalize this approach by introducing random gates. They have theoretical performances nearly as good as parity checks, but they offer the great advantage that the encoding can be done in linear time using the survey inspired decimation algorithm, a powerful algorithm for constraint satisfaction problems derived from statistical physics.