Entanglement purification is an essential component of quantum repeaters, as it can improve the fidelity of the distributed entangled states and mitigate the effects of the noisy channel. Successful purification yields entangled states with increased fidelity, whereas failed events can still retain residual entanglement that remains usable for further purification when the error rates of the two degrees of freedom (DOFs) are unbalanced. In this paper, we demonstrate a single-copy entanglement purification scheme based on hyperentanglement using silicon chips and experimentally observe the presence of residual entanglement. Leveraging the reconfigurability of integrated photonics, our scheme ensures that, under bit-flip noise acting on the two DOFs, residual entanglement suitable for further purification can always be obtained, regardless of which DOF has the higher error rate. Our results demonstrate the advantages of integrated photonics for quantum information processing and provide guidance for the optimized utilization of entanglement resources in on-chip entanglement purification and future quantum repeater systems.
Entanglement purification is an essential component of quantum repeaters, as it can improve the fidelity of the distributed entangled states and mitigate the effects of the noisy channel. Successful purification yields entangled states with increased fidelity, whereas failed events can still retain residual entanglement that remains usable for further purification when the error rates of the two degrees of freedom (DOFs) are unbalanced. In this paper, we demonstrate a single-copy entanglement purification scheme based on hyperentanglement using silicon chips and experimentally observe the presence of residual entanglement. Leveraging the reconfigurability of integrated photonics, our scheme ensures that, under bit-flip noise acting on the two DOFs, residual entanglement suitable for further purification can always be obtained, regardless of which DOF has the higher error rate. Our results demonstrate the advantages of integrated photonics for quantum information processing and provide guidance for the optimized utilization of entanglement resources in on-chip entanglement purification and future quantum repeater systems.
Abstract Quantum repeaters are employed in quantum communication to overcome the long-distance transmission loss of quantum states. The quantum repeater is based on various key technologies, including quantum entanglement swapping, quantum memory, and entanglement purification. In particular, quantum purification can distil high-quality entanglement from the degraded entangled states which is propagating through noisy quantum communication channels. Although previous reports have demonstrated on-chip entanglement swapping and teleportation through the less-noisy channel, current entanglement purification experiments still rely on off-chip discrete devices, leading to limitations on scalability, stability and controllability. In this paper, for the first time, we demonstrated chip-to-chip hyperentanglment distribution and quantum entanglement purification based on integrated silicon chips. Path-encoded high-dimensional entangled photon pairs are produced on the chip, converted to fibre-based polarization-spatial hyperentanglement by grating couplers, distributed to the receiver silicon chip, and finally purified by consuming the spatial degree of freedom. Our purification scheme by integrated photonics finished the important puzzle of on-chip quantum repeater, which will promote the realization of the quantum repeater based on integrated photonics.
Quantum repeaters are employed in quantum communication to overcome the long-distance transmission loss of quantum states. The quantum repeater is based on various key technologies, including quantum entanglement swapping, quantum memory, and entanglement purification. In particular, quantum purification can distil high-quality entanglement from the degraded entangled states which is propagating through noisy quantum communication channels. Although previous reports have demonstrated on-chip entanglement swapping and teleportation through the less-noisy channel, current entanglement purification experiments still rely on off-chip discrete devices, leading to limitations on scalability, stability, and controllability. In this paper, for the first time, we demonstrated chip-to-chip hyperentanglement distribution and quantum entanglement purification based on integrated silicon chips. Path-encoded high-dimensional entangled photon pairs are produced on the chip, converted to fibre-based polarization-spatial hyperentanglement by grating couplers, distributed to the receiver silicon chip, and finally purified by consuming the spatial degree of freedom. Our purification scheme by integrated photonics finished the last puzzle of on-chip quantum repeater, which will promote the realization of the quantum repeater based on integrated photonics.
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.
Linear quantum repeater chains based on Werner-state purification (the BBPSSW protocol) and entanglement swapping (the BDCZ scheme) are fundamental to entanglement distribution in quantum networks. However, they operate under a stringent operation reliability threshold and rely on resource-intensive recurrence purification rounds, each consuming two entangled pairs to probabilistically produce one. In the literature, hyperentanglement has been proposed to exploit multiple degrees of freedom (DOF), such as polarisation and spatial modes, to encode independent entangled states within a single photon pair. This has led to the definition of DAEPP (DOF-Assisted Entanglement Purification Protocol), which we propose to integrate with the BDCZ scheme, resulting in a chain protocol that we call DAHR (DOF-Assisted Hyperentanglement Repeater). The DAEPP step distils the fidelity of a DOF by consuming other(s). In this work, we propose and analyse a DAHR variant which integrates DAEPP at every segment of an end-to-end path combined with BDCZ. We derive a closed-form end-to-end fidelity recursion that embeds single-segment DAEPP into the BDCZ scheme and give a strict resource lower bound for any BDCZ baseline utilising BBPSSW purification to match DAHR's per-segment effective fidelity. At a representative asymmetric operating point informed by prior experiment, we show numerically that matching DAHR's single-photon-pair performance requires two to three rounds of BBPSSW purification. Additionally, below a critical operation reliability, no amount of BBPSSW rounds matches DAHR's one DAEPP round performance.
Entanglement purification is to distill high-quality entanglement from low-quality entanglement. Entanglement purification determines the efficiency and communication rates and plays a key role in quantum repeaters and long-distance quantum communications. Existing entanglement purification protocols and proof of principle experiments usually choose two identical input pairs. They are limited to focus on the successful purification case to obtain high-quality entangled states and discard the remained items if the purification fails. Recent entanglement purification theory [Opt. Express 28, 2291 (2020)OPEXFF1094-408710.1364/OE.383499] for arbitrary nonidentical input mixed states indicated that the discarded items may have residual entanglement and can be reused to increase the yield of entanglement purification, while the successful purification may not obtain a high-quality entangled state. In this Letter, using hyperentanglement, we design and experimentally demonstrate an entanglement purification protocol with nonidentical input mixed states. For the first time, we experimentally confirm the existence of residual entanglement in different error models. Furthermore, we illustrate that successful purification may decrease the fidelity of purified entangled states. We also demonstrate the approach of optimal entanglement purification. Our proof of principle results have potential applications in future high-efficiency and long-distance quantum communication.