PRL Editor's Pick Ma Xiongfeng's group at Tsinghua University makes important progress in entanglement detection research

Recently, Xiongfeng Ma's research group at the School of Cross-Information, Tsinghua University has made important progress in the research work on entanglement detection protocols, demonstrating the nonexistence of both efficient and powerful single-copy entanglement criterion.

Quantum information technology is expected to demonstrate advantages in various information processing tasks. Currently, we are at the stage of "noisy medium-scale quantum devices": researchers can manipulate up to 50 to 200 quantum bits to demonstrate quantum advantages. For these devices, the generation and detection of entanglement is an important benchmark for the quality of the device. Counter-intuitively, however, even though entangled states occupy almost the entire quantum state space, the difficulty of entanglement detection is still beyond prediction.

Schematic diagram of state space and entanglement witnessing

Among the various entanglement criterions, entanglement witnessing is the most straightforward and the most frequently used in experiments. However, much evidence suggests that entanglement witnessing is only effective with precise prior knowledge of the target quantum state. Unpredictable noise in state preparation can significantly reduce the probability of successful entanglement witnessing.

To address this problem, researchers have developed nonlinear entanglement witnessing, such as the well-known partial transposition witnessing. Although more effective than entanglement witnessing, these nonlinear criterions rely heavily on quantum state cascading. However, state lamination requires exponentially more resources and is often experimentally unaffordable. In the past decades, researchers have worked to optimize these powerful nonlinear entanglement criterion to reduce experimental consumption. In recent years, a class of criteria based on moments and random measurements has been proposed that can do the job of detecting entanglement without doing quantum state lamination, well meeting the limitations of current quantum devices. Although much more efficient than state lamination, these methods still require exponentially more resource consumption.

The above facts show an interesting phenomenon: efficient entanglement criterion is often not powerful enough, while powerful entanglement criterion cannot be efficiently implemented experimentally. In this work, researchers in Xiongfeng Ma's group investigate the above observation theoretically. Through a systematic approach to evaluate the detection capability of the entanglement criterion, they found a limit between the efficiency and effectiveness of the entanglement criterion. For a random system coupled to the environment, they demonstrated that any entanglement criterion based on single-copy measurements requires exponentially more measurements to effectively detect entanglement. Otherwise, the detection capability of the criterion will double exponentially decay. Moreover, if joint multi-copy measurements are allowed, the effectiveness of the entanglement criterion can be improved exponentially, implying a quantum advantage in the entanglement detection problem.

The detectability of the four entanglement criteria varies with the dimensionality of the environment, with an exponentially decreasing trend in the high-dimensional case

The paper, "Fundamental Limitation on the Detectability of Entanglement," was recently published in Physical Review Lett. 129, 230503 (2022), and selected as Editors' Suggestions.

The corresponding author of the paper is Associate Professor Xiongfeng Ma of the School of Cross-Information, Tsinghua University. Pengyu Liu, a 2019 undergraduate student in the School of Cross-Information, Tsinghua University, is the first author of the article. Other authors include Zhenhuan Liu, a 2020 PhD student in the School of Cross-Information, and Shu Chen, a 2019 undergraduate student in the School of Cross-Information. This project was supported by the National Natural Science Foundation of China and the National Key Research and Development Program.

Link to the paper:

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.230503