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Annalen der Physik

Purification for Hybrid Entanglement between Discrete‐ and Continuous‐Variable States

Cheng‐Chen Luo, Lan Zhou, Wei Zhong, Ming‐Ming Du, Xi‐Yun Li, Yu‐Bo Sheng

Published Jan 4, 2024• 2 citations
Publisher

Abstract

Abstract Hybrid entangled states (HES) have attracted significant attention and been utilized in various quantum information processing applications. However, like many other entangled states, maximally entangled HES may degrade to mixed states due to environmental noise and operational imperfections. In this paper, a hybrid entanglement purification protocol (HEPP) for the HES, which consists of photon‐number state and coherent state is proposed. This HEPP is designed to effectively purify a bit‐flip error occurring in any qubit of the HES. Furthermore, HEPP is extended to a general condition, say, the multi‐party scenario, and integrates the generation of HES into the HEPP. Moreover, if different initial mixed states are chosen, then the residual entanglement can be utilized to distill high‐quality entanglement. The HEPP has important applications in the future quantum information processing field.

DOI
10.1002/andp.202300494

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Abstract Hybrid entangled states (HES) have attracted significant attention and been utilized in various quantum information processing applications. However, like many other entangled states, maximally entangled HES may degrade to mixed states due to environmental noise and operational imperfections. In this paper, a hybrid entanglement purification protocol (HEPP) for the HES, which consists of photon‐number state and coherent state is proposed. This HEPP is designed to effectively purify a bit‐flip error occurring in any qubit of the HES. Furthermore, HEPP is extended to a general condition, say, the multi‐party scenario, and integrates the generation of HES into the HEPP. Moreover, if different initial mixed states are chosen, then the residual entanglement can be utilized to distill high‐quality entanglement. The HEPP has important applications in the future quantum information processing field.
Abstract Hybrid entangled states (HESs), which involve different particles with various degrees of freedom, have garnered significant attention and been applied in a wide range of quantum technologies. However, similar to other categories of entanglement, maximally HESs inevitably degrade to mixed states due to the environmental noise and operational imperfections. To address the degradation problem, measurement-based entanglement purification offers a feasible and robust solution alternative to conventional gate-based purification methods. In this paper, we propose a measurement-based hybrid entanglement purification protocol (MB-HEPP) for a certain kind of HES which consists of polarization photons and coherent states. We extend our methodology to several conditions, such as the multi-copy and multi-party scenarios, and the photon-loss condition. Compared with previous HEPPs, this protocol has several advantages. First, it does not depend on post-selection and the purified HESs can be retained for further application. Second, it does not require the Bell state measurement, but only uses the parity check with conventional linear optical elements, which makes it have the higher success probability and more feasible. Our MB-HEPP has potential applications in future heterogeneous quantum networks.
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.
Abstract Entanglement purification is an important method to guarantee the fidelity of long‐distance quantum communication. Here, a general entanglement purification protocol (EPP) for mixed state with bit‐flip error and phase‐flip error is proposed, resorting to unilateral operations and a controlled‐phase‐flip (CPF) gate. The CPF gate is working with a high fidelity under balance condition of quantum dot embedded in a double‐sided optical cavity. This general EPP scheme can purify the mixed state with both bit‐flip error and phase‐flip error to a high fidelity entangled state relatively fast in some regimes, owing to the unilateral operations and high‐fidelity CPF gate, which can largely decrease the resource consumption. This general EPP provides a convenient way for increasing the entanglement of different quantum systems, which has great potential for guaranteeing the fidelity of long‐distance quantum communication in the future.
Abstract Entanglement purification is a powerful way to protect the quality of entangled system from channel noise and environment noise. A universal highly effective entanglement purification protocol with single‐copy hyperentangled state (H‐UHEPP) is proposed for distillable mixed entangled states with bilateral controlled‐not gate operations, bilateral asymmetrical rotation operations and single photon Bell‐state measurements, where all of these operations and measurements are easy to implement in polarization, spatial and time‐bin degrees of freedom (DOFs) of photon system. This H‐UHEPP, which requires only one pair of hyperentangled photons and simple unitary operations on three DOFs of a photon, can significantly enhance the fidelity of the purified state compared with the previous works. As a consequence, H‐UHEPP can speed up the entanglement purification process and reduce the resource consumption, which makes it useful in future quantum information processing.
The entangled coherent states (ECSs) have been widely used to realize quantum information processing tasks. However, the ECSs may suffer from photon loss and decoherence due to the inherent noise in quantum channel, which may degrade the fidelity of ECSs. To overcome these obstacles, we present a measurement-based entanglement purification protocol (MBEPP) for ECSs to distill some high-quality ECSs from a large number of low-quality copies. We first show the principle of this MBEPP without considering the photon loss. After that, we prove that this MBEPP is feasible to correct the error resulted from the photon loss. Additionally, this MBEPP only requires to operate the Bell state measurement without performing local two-qubit gates on the noisy pairs and the purified high-quality ECSs can be preserved for other applications. This MBEPP may have application potential in the implementation of long-distance quantum communication.
Entanglement purification is a powerful method to distill the high-quality entanglement from low-quality entanglement. In the paper, we propose an efficient two-step entanglement purification protocol (EPP) for the polarization entanglement by using only one copy of two-photon hyperentangled state in polarization, spatial-mode, and time-bin DOFs. We suppose that the entanglement in all DOFs suffer from channel noise. In two purification steps, the parties can reduce the bit-flip error and phase-flip error in polarization DOF by consuming the imperfect entanglement in the spatial-mode and time-bin DOFs, respectively. This EPP effectively reduces the consumption of entanglement pairs and the experimental difficulty. Moreover, if consider the practical photon transmission and detector efficiencies, our EPP has much higher purification efficiency than previous recurrence EPPs. Meanwhile, when one or two purification steps fail, the distilled mixed state may have residual entanglement. Taking use of the residual entanglement, the parties may still distill higher-quality polarization entanglement. Even if not, they can still reuse the residual entanglement in the next purification round. The existence of residual entanglement benefits for increasing the yield of the EPP. All the above advantages make our EPP have potential application in future quantum information processing.