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Physical Review A

Error identification entanglement purification for stationary system using high-dimensional entanglement

Ji Qi, Ke Li, Zhe Yang, Rui‐Yang Yuan, Bao‐Cang Ren

Published Apr 23, 2024• 15 citations
Publisher

Abstract

High-fidelity entanglement plays an important role in quantum networks for guaranteeing the integrity of quantum information processing. We present an error identification entanglement purification protocol (EIEPP) for maintaining high-fidelity entanglement of stationary systems. In EIEPP, the hybrid controlled-x gate for stationary systems and high-dimensional spatial-mode state of photons has been constructed using a stationary-whispering gallery mode resonator-waveguides system, and it is used to construct an error number gate (ENG) and error position gate (EPG) for noisy entangled stationary systems. Using ENG and EPG, the stationary systems with errors are discarded according to the measurement results of high-dimensional entangled photon states, and typically high-fidelity entangled states of stationary systems can be achieved with high yield in both ideal and practical situations. This EIEPP has superior performance for stationary systems with amplitude damping noise, and it is also applicable for stationary systems with other types of noise.

DOI
10.1103/physreva.109.042423

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High-fidelity entanglement plays an important role in quantum networks for guaranteeing the integrity of quantum information processing. We present an error identification entanglement purification protocol (EIEPP) for maintaining high-fidelity entanglement of stationary systems. In EIEPP, the hybrid controlled-x gate for stationary systems and high-dimensional spatial-mode state of photons has been constructed using a stationary-whispering gallery mode resonator-waveguides system, and it is used to construct an error number gate (ENG) and error position gate (EPG) for noisy entangled stationary systems. Using ENG and EPG, the stationary systems with errors are discarded according to the measurement results of high-dimensional entangled photon states, and typically high-fidelity entangled states of stationary systems can be achieved with high yield in both ideal and practical situations. This EIEPP has superior performance for stationary systems with amplitude damping noise, and it is also applicable for stationary systems with other types of noise.
The efficient generation of high-fidelity entangled states is the key element for long-distance quantum communication, quantum computation, and other quantum technologies, and at the same time the most resource-consuming part in many schemes. We present a class of entanglement-assisted entanglement purification protocols that can generate high-fidelity entanglement from noisy, finite-size ensembles with improved yield and fidelity as compared to previous approaches. The scheme utilizes high-dimensional auxiliary entanglement to perform entangling nonlocal measurements and determine the number and positions of errors in an ensemble in a controlled and efficient way, without disturbing the entanglement of good pairs. Our protocols can deal with arbitrary errors, but are best suited for few errors, and work particularly well for decay noise. Our methods are applicable to moderately sized ensembles, as will be important for near term quantum devices.
We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about the number and positions of errors in the noisy ensemble in an explicit and controlled way, thereby reducing the amount of noise in the ensemble and purifying the remaining states. This allows us to design entanglement purification protocols for any number of copies that work particularly well for a small number of expected errors, i.e., high fidelity of initial states. The main tool is a counter gate with which the required nonlocal information can be transferred into the high-dimensional entangled qudit auxiliary states. We compare our schemes to standard recurrence protocols that operate on pairs of copies, and hashing and breeding protocols that operate on a (asymptotically) large number of copies. Our protocols interpolate between these two regimes, leading to higher achievable fidelity and yield. We illustrate our approach for bipartite qubit states and generalize it to purify multiparty GHZ states.
High-dimensional quantum entanglement offers significant advantages over its two-dimensional counterparts in various quantum information processing tasks. We propose a scalable method for implementing an arbitrary high-dimensional entanglement purification protocol (HDEPP) using path superposition. By selecting appropriate single-qudit gates, qudit-flip errors and phase-flip errors can be purified. Counterintuitively, the HDEPP becomes more robust for higher-dimensional systems and exhibits enhanced purification fidelity as the dimension increases. Our HDEPP not only requires fewer operational resources but also in principle can achieve unity fidelity through multiple rounds of iteration. Furthermore, we develop feasible optical schemes to purify the frequency degree of freedom of photons suffering from qudit-flip and phase-flip errors using hyperentanglement. This work paves the way toward high-dimensional quantum communication and quantum networks.
Abstract The distribution of maximal entanglement stands as a pivotal technique in long-distance practical quantum communication. Specifically, achieving high-fidelity entanglement distribution leans upon efficacious entanglement purification and entanglement concentration. In this paper, we materialize error-rejecting nonlocal entanglement purification protocol (EPP) and entanglement concentration protocol (ECP) for solid-state emitter systems assisted by the scattering property of photon-emitter in one-dimensional waveguide. The parity-check gates of both the EPP and ECP can herald the faulty events with the help of the detectors that click, so they are accomplished, in principle, with unity fidelities, which are conducive to implement two protocols. Moreover, additional emitters are unnecessary except a single photon.
Multipartite entanglement plays an important role in controlled quantum teleportation, quantum secret sharing, quantum metrology and some other important quantum information branches. However, the maximally multipartite entangled state will degrade into the mixed state because of the noise. We present an efficient multipartite entanglement purification protocol (EPP) which can distill the high quality entangled states from low quality entangled states for N-photon systems in a Greenberger-Horne-Zeilinger (GHZ) state in only linear optics. After performing the protocol, the spatial-mode entanglement is used to purify the polarization entanglement and one pair of high quality polarization entangled state will be obtained. This EPP has several advantages. Firstly, with the same purification success probability, this EPP only requires one pair of multipartite GHZ state, while existing EPPs usually require two pairs of multipartite GHZ state. Secondly, if consider the practical transmission and detector efficiency, this EPP may be extremely useful for the ratio of purification efficiency is increased rapidly with both the number of photons and the transmission distance. Thirdly, this protocol requires linear optics and does not add additional measurement operations, so that it is feasible for experiment. All these advantages will make this protocol have potential application for 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.