Entanglement distillation is a well-studied problem in quantum information, where one typically starts with $n$ noisy Bell pairs and distills $k$ Bell pairs of higher fidelity. While distilling Bell pairs is the canonical setting, it is important to study the distillation of multipartite entangled states because these can be useful for realizing distributed algorithms on quantum networks. In this paper, we study the distillation of GHZ states using quantum error correcting codes (QECCs). Using the stabilizer formalism, we begin by explaining the QECC-based Bell pair distillation protocol in arXiv:0708.3699, which relies particularly on the transpose symmetry between Alice's and Bob's qubits in Bell states. Extending this idea, we show that, given $n$ GHZ states, performing a matrix on Alice's qubits is equivalent to performing a "stretched" version of the transpose of the matrix on the qubits of Bob and Charlie. We call this mapping to the stretched version of the matrix the GHZ-map, and show that it is an algebra homomorphism. Using this property, we show that Alice projecting her qubits onto an $[[n,k]]$ stabilizer code implies the simultaneous projection of Bob's and Charlie's qubits onto an induced $[[2n,k]]$ stabilizer code. Guided by this insight, we develop a GHZ distillation protocol based on local operations and classical communication that uses any stabilizer code. Inspired by stabilizer measurements on GHZ states, we also develop a new algorithm to generate logical Pauli operators of any stabilizer code and use it in the protocol. Since quantum codes with finite rate and almost linear minimum distance have recently been discovered, this paper paves the way for high-rate high-output-fidelity GHZ distillation. We provide simulation results on the $5$-qubit perfect code to emphasize the importance of the placement of a certain local Clifford operation in the protocol.
Stabilizer Statistical Mechanics: A Framework for Efficient Quantification and Classification of Magic States
LG Electronics Toronto AI Lab（LG电子多伦多人工智能实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654（MajuLab，CNRS-UNS-NUS-NTU国际联合研究单元，UMI 3654）；National Institute of Education, Nanyang Technological University（南洋理工大学国立教育学院）
Necessary and sufficient criterion for k-separability of N-qubit noisy GHZ states
一个多体纠缠态有许多种不同的纠缠，这些纠缠由粒子的数目决定。多体纠缠最基本的例子是白噪声中多量子比特Greenberger-Horne-Zeilinger（GHZ）态的纠缠。我们明确地构造了这些状态的纠缠证人与GHZ态的稳定剂生成器。对于白噪声中的$N$量子比特GHZ态，我们证明了当任意$N$和$k$被分成$k$和$N\leq 2k-1$时，它是可分离的充要条件.该判据涵盖了白噪声中$% N $ -量子比特GHZ态的一半以上的部分纠缠。对于其余的多体纠缠问题，我们给出了一种方法来获得分离性的充分条件。作为应用，我们考虑了$N$量子比特GHZ态作为简并量子码通过去极化信道的码字。我们发现当量子信道容量从正减小到零时，输出态既不是真正纠缠的，也不是完全可分的。
Zeno-Enhanced Probabilistic Error Cancellation with Quantum Error Detection Codes
Tsinghua University（清华大学）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Hefei National Laboratory（合肥国家实验室）
Certifying optimal device-independent quantum randomness in quantum networks
Hangzhou Dianzi University（杭州电子科技大学）；Zhejiang Provincial Key Laboratory of Sensitive Data Security and Confidentiality Governance（浙江省敏感数据安全与保密治理重点实验室）；The University of Hong Kong（香港大学）
Fault-tolerant modular quantum computing with surface codes using single-shot emission-based hardware
QuTech, Delft University of Technology（代尔夫特理工大学）；Graduate School of Informatics, Kyoto University（京都大学情报大学院）；Department of Electronics and Electrical Engineering, Keio University（庆应义塾大学电子电气工程系）；Networked Quantum Devices Unit, Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学网络量子设备单元）；National Institute of Information and Communications Technology (NICT)（信息通信研究机构）
Generalised Bit-Vector Abstractions for Formal Verification of Quantum Error-Detection and Entanglement Circuits over {H,X,C-NOT}: CSS Constructions, Soundness, and Mutation-Based Validation
Weight-four parity checks with silicon spin qubits
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学量子技术与开利纳米科学研究所）；Netherlands Organization for Applied Scientific Research (TNO)（荷兰应用科学研究组织（TNO））
Fault-tolerant distributed quantum computing with a single nucleus per node
Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡赫物理研究所，耶路撒冷希伯来大学）；Yale Quantum Institute & Department of Applied Physics, Yale University（耶鲁量子研究所与应用物理系，耶鲁大学）；AWS Center for Quantum Computing（亚马逊云科技量子计算中心）
Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
University of Cologne（科隆大学）；University of Geneva（日内瓦大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
