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International Journal of Quantum Information

An efficient approach for quantum entanglement purification

Swathi Mummadi, Bhawana Rudra

Published Feb 28, 2022• 16 citations
Publisher

Abstract

Entanglement plays a major role in quantum information process and is a principal resource for various quantum applications like quantum teleportation, quantum key distribution, quantum communication, etc. Strong entangled pairs are required for efficient information process but system impurities during the transportation diminishes the entanglement by reducing the fidelity of the entangled pair. In order to reduce this, purification techniques can be used. In this paper, we propose an efficient entanglement purification method to distill the entanglement using entanglement swapping. The proposed method increases the fidelity of the entanglement and can be a proficient for various applications of quantum computing.

DOI
10.1142/s0219749922500046

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Entanglement plays a major role in quantum information process and is a principal resource for various quantum applications like quantum teleportation, quantum key distribution, quantum communication, etc. Strong entangled pairs are required for efficient information process but system impurities during the transportation diminishes the entanglement by reducing the fidelity of the entangled pair. In order to reduce this, purification techniques can be used. In this paper, we propose an efficient entanglement purification method to distill the entanglement using entanglement swapping. The proposed method increases the fidelity of the entanglement and can be a proficient for various applications of quantum computing.
Quantum communication technology provides an absolute security guarantee for information transmitted between quantum applications. To establish practical quantum networks, providing entangled pairs of stable quality, suitable for varying distances, is crucial. However, due to the inherent losses and imperfections of the operations during the entanglement distribution process, the fidelity of end-to-end entangled pairs will be greatly reduced. Consequently, establishing fidelity-guaranteed entangled pairs will be challenging. In this work, we introduce an entanglement distribution method that ensures the fidelity requirements of applications across different distances, while maintaining high efficiency. The method first decomposes the end-to-end fidelity requirements to target fidelity for purification at each link, based on the worst-case consumption. Then it performs multiple-round symmetrical entanglement purification based on the backup scheme to purify each entangled pair to the target value. The experimental results indicate that the scheme has acceptable performance in resource consumption and great feasibility while ensuring high efficiency.
In order to perform faithfully quantum communication protocols such as quantum teleportation, superdense coding, quantum key distribution, and quantum secret sharing, we need the entanglement purification process to make a maximal entanglement out of many copies of the partially entangled pairs by using local operations and classical communication. In this dissertation,\nwe analyze the efficiency of several entanglement purification protocols for qubit states and qudit states, and present a new efficient entanglement purification protocol. Furthermore, we show that our method can be applied to the existing best protocol\nso as to improve the efficiency.
High-quality long-distance entanglement is essential for both quantum communication and scalable quantum networks. Entanglement purification is to distill high-quality entanglement from low-quality entanglement in a noisy environment and it plays a key role in quantum repeaters. The previous significant entanglement purification experiments require two pairs of low-quality entangled states and were demonstrated in tabletop. Here we propose and report a high-efficiency and long-distance entanglement purification using only one pair of hyperentangled state. We also demonstrate its practical application in entanglement-based quantum key distribution (QKD). One pair of polarization spatial-mode hyperentanglement was distributed over 11 km multicore fiber (noisy channel). After purification, the fidelity of polarization entanglement arises from 0.771 to 0.887 and the effective key rate in entanglement-based QKD increases from 0 to 0.332. The values of Clauser-Horne-Shimony-Holt inequality of polarization entanglement arises from 1.829 to 2.128. Moreover, by using one pair of hyperentanglement and deterministic controlled-NOT gates, the total purification efficiency can be estimated as 6.6×10^{3} times than the experiment using two pairs of entangled states with spontaneous parametric down-conversion sources. Our results offer the potential to be implemented as part of a full quantum repeater and large-scale quantum network.
Quantum networks rely on the efficient distribution of entanglement to enable long-distance quantum communication and information processing. A key challenge in these networks is the design of routing protocols capable of maintaining high quality entanglement in the presence of noise, decoherence, and imperfect operations, which progressively degrade the fidelity of entangled states through entanglement swapping. Entanglement purification provides an effective mechanism to mitigate this degradation at the cost of additional resources. In this work, we study purification-aware quantum routing and formulate the problem of selecting optimal purification strategies as an optimization task. By employing dynamic programming techniques, we identify strategies that optimally balance resource consumption and end-to-end fidelity, demonstrating the effectiveness of our approach across different scenarios.
We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.
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.