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Physical Review A

Distillation of lossy hyperentangled states

Danyang Chen, Zhi Lin, Ming Yang, Qing Yang, Xue-Ping Zang, Zhuo‐Liang Cao

Published Aug 28, 2020• 7 citations
Publisher

Abstract

Hyperentanglement has a higher information density than conventional single-degree-of-freedom entanglement, which has attracted much attention due to its fascinating applications in quantum communication. However, since the inevitable interactions between quantum entangled systems and the environment will drive hyperentangled systems into less hyperentangled states or even mixed hyperentangled states, the efficiency and security of quantum communication will be greatly depressed. The currently existing distillation protocols are not universal, i.e., they only work for the lossy hyperentangled states in specific systems. In this paper, based on local positive-operator-valued measures (POVMs), we present a distillation protocol for lossy hyperentangled photonic Bell and Greenberger-Horne-Zeilinger (GHZ) states. The intrinsic property of our protocol is twofold, i.e., the POVM nature of the protocol guarantees that the protocol is a universal one, and the distillation operation on only one of the two degrees of freedom (DOFs) can enhance the fidelity of the system in both DOFs. Furthermore, in the implementation level, our hyperentanglement distillation protocol (HEDP) has other two merits: no auxiliary local entanglement resources and sophisticated single-photon detectors are required, and only one copy of the lossy state will be operated in each distillation round, which show that our HEDPs are relatively simple and feasible.

DOI
10.1103/physreva.102.022425

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Hyperentanglement has a higher information density than conventional single-degree-of-freedom entanglement, which has attracted much attention due to its fascinating applications in quantum communication. However, since the inevitable interactions between quantum entangled systems and the environment will drive hyperentangled systems into less hyperentangled states or even mixed hyperentangled states, the efficiency and security of quantum communication will be greatly depressed. The currently existing distillation protocols are not universal, i.e., they only work for the lossy hyperentangled states in specific systems. In this paper, based on local positive-operator-valued measures (POVMs), we present a distillation protocol for lossy hyperentangled photonic Bell and Greenberger-Horne-Zeilinger (GHZ) states. The intrinsic property of our protocol is twofold, i.e., the POVM nature of the protocol guarantees that the protocol is a universal one, and the distillation operation on only one of the two degrees of freedom (DOFs) can enhance the fidelity of the system in both DOFs. Furthermore, in the implementation level, our hyperentanglement distillation protocol (HEDP) has other two merits: no auxiliary local entanglement resources and sophisticated single-photon detectors are required, and only one copy of the lossy state will be operated in each distillation round, which show that our HEDPs are relatively simple and feasible.
High-dimensional hyperentangled states, serving as crucial physical resources in quantum communication, have attracted significant attention due to their exceptional properties (e.g., higher information density) compared to conventional two-dimensional single-degree-of-freedom entanglement. However, practical quantum entanglement systems inevitably suffer from environmental interactions, resulting in their degradation into partially entangled pure states or even mixed states, thereby significantly compromising the efficiency and security of quantum communication. Consequently, improving entanglement preservation in noisy systems emerges as a pivotal challenge in realizing fault-tolerant quantum networks. We propose two universal distillation schemes based on local positive-operator-valued measures (POVMs) for single-copy $(2\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4)$-dimensional hyperentangled photons. These schemes effectively suppress photon vacuum errors induced by transmission losses and are constructed using spatial-mode and polarization-based POVM measurements, respectively. Our results demonstrate that the spatial-mode-based scheme outperforms its polarization-based counterpart in terms of fidelity and success probability. Remarkably, we discover that with appropriate POVM parameters, the fidelity range of amplitude-damped noisy states can be expanded to cover almost all parameter spaces. Due to the universal applicability of POVM measurements, which require neither auxiliary entanglement nor complex detectors and operate on single copies of imperfect states in each purification round, our scheme provides an experimentally feasible solution for distilling high-dimensional hyperentangled photonic states.
As the interaction between the photons and the environment which will make the entangled photon pairs in less entangled states or even in mixed states, the security and the efficiency of quantum communication will decrease. We present an efficient hyperentanglement purification protocol that distills nonlocal high-fidelity hyper-entangled Bell states in both polarization and spatial-mode degrees of freedom from ensembles of two-photon system in mixed states using linear optics. Here, we consider the influence of the photon loss in the channel which generally is ignored in the conventional entanglement purification and hyperentanglement purification (HEP) schemes. Compared with previous HEP schemes, our HEP scheme decreases the requirement for nonlocal resources by employing high-dimensional mode-check measurement, and leads to a higher fidelity, especially in the range where the conventional HEP schemes become invalid but our scheme still can work.
Quantum communication is based on the generation of quantum states and exploitation of quantum resources for communication protocols. Currently, photons are considered as the optimal carriers of information, because they enable long-distance transition with resilience to decoherence and they are relatively easy to create and detect. Entanglement is a fundamental resource for quantum communication and information processing, and it is of particular importance for quantum repeaters. Hyperentanglement, a state where parties are entangled with two or more degrees of freedom (DoFs) simultaneously, provides an important additional resource because it increases data rates and enhances error resilience. However, in photonics, the channel capacity, i.e., the ultimate throughput, is fundamentally limited when dealing with linear elements. We propose a technique for achieving higher transmission rates for quantum communication by using hyperentangled states, based on multiplexing multiple DoFs on a single photon, transmitting the photon, and eventually demultiplexing the DoFs to different photons at the destination, using Bell state measurements. Following our scheme, one can generate two entangled qubit pairs by sending only a single photon. The proposed transmission scheme lays the groundwork for novel quantum communication protocols with higher transmission rates and refined control over scalable quantum technologies.
Abstract The information content of a photon system can be extended by hyperentanglement, but the quality of hyperentanglement will be decreased by the complicated transmission loss and channel noise in quantum information processing. Here, an efficient measurement‐based hyperentanglement distillation protocol (MB‐HDP) is presented for depressing the effects of complicated transmission loss and channel noise on hyperentanglement. In the MB‐HDP, the nonlocal lossy and distortion photon states are coupled to local hyperentangled Greenberger–Horne–Zeilinger (GHZ) states using parity measurement and qubit amplification device, and the decoherence caused by bit‐flip (phase‐flip) error, diverse transmission coefficients and transmission loss can be depressed by the successful measurement results, which can increase the quality of nonlocal hyperentangled photon state. This MB‐HDP broadens the application scope of hyperentanglement distillation to nonlocal lossy and distortion photon state with a lower degree of entanglement. In addition, the MB‐HDP can further improve the quality of nonlocal hyperentangled photon state by coupling multiple copies of lossy and distortion hyperentangled photon state with local hyperentangled GHZ states. This work demonstrates the ability of measurement‐based method for ensuring the quality of nonlocal hyperentanglement, which can improve the integrity and capacity of long‐distance quantum information processing.
Entanglement distillation has many applications in quantum information processing and is an important tool for improving the quality and efficiency of quantum communication, cryptography, computing, and simulation. We propose an entanglement distillation scheme using only one pair of polarization-frequency hyperentangled photons, which can be equivalently viewed as containing two pairs of entangled logical qubits: a pair of polarization-entangled qubits and a pair of frequency-entangled qubits. To perform the required CNOT operation between the two qubits we consider the use of a polarization-dependent frequency converter. Compared to past methods of entanglement distillation that relied on polarization and spatial-mode/energy-time degree of freedom, the utilization of frequency-encoded qubits offers an advantage in that it is immune to bit-flip errors when the channel is linear. After distillation, the fidelity of polarization entanglement can be significantly improved by sacrificing the frequency degree of freedom. Through simulation, we show that high fidelity gains, large yield, and high distillation rate can be achieved. Our distillation scheme is simple to implement with current technologies, compatible with existing telecommunication fiber networks, and is a promising approach for achieving efficient quantum communication.
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.