发表机构
Technology Innovation Institute (TII); Institute for Interdisciplinary Information Sciences, Tsinghua University; Dahlem Center for Complex Quantum Systems, Freie Universität Berlin; Yau Mathematical Sciences Center, Tsinghua University; Helmholtz-Zentrum Berlin für Materialien und Energie（技术创新研究所; 清华大学交叉信息研究院; 柏林自由大学达勒姆复杂量子系统中心; 清华大学丘成桐数学科学中心; 赫尔霍兹柏林材料与能源中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用纠缠高效认证时间反演对称性，证明最大纠缠探针和SWAP测量可将查询复杂度降至常数，建立了纠缠与时间反演对称性的定量联系。
AI 中文摘要
时间反演对称性是物理学的基本原理，描述物理定律在时间方向反转下的不变性。我们利用仅前向访问和可信量子操作，构建了一个针对这种反幺正对称性的类贝尔不等式测试：纠缠将时间上的输入-输出关系转化为可测量的空间交换对称性。对于n量子比特酉动力学，我们证明，对于任何经典自适应协议，可靠区分时间反演对称的圆形系综与哈达玛随机动力学需要Ω(min{2^{n/2},2^{n-e}})次查询。这里，e=min{e_s,e_m}，其中e_s和e_m分别表示探针和测量的对数纠缠负性。最大纠缠探针和SWAP测量将此成本降低到常数次查询。此外，我们为任意固定的、兼容的探针和测量开发了一种时间反演对称性测试，将其查询复杂度与其对数负性相关联，并通过优化探针和测量在高纠缠区域匹配下界缩放。我们的结果建立了纠缠与时间反演对称性之间的定量联系，架起了量子信息科学与基础物理学两个核心概念之间的桥梁。
英文摘要
Time-reversal symmetry is a fundamental principle of physics describing the invariance of physical laws under reversal of the direction of time. We formulate a Bell-inequality-like test of this antiunitary symmetry using only forward access and trusted quantum operations: entanglement converts temporal input--output relations into measurable spatial exchange symmetry. For $n$-qubit unitary dynamics, we prove that reliably distinguishing the time-reversal-symmetric circular ensembles from Haar-random dynamics requires $Ω(\min\{2^{n/2},2^{n-e}\})$ queries for any classically adaptive protocol. Here, $e=\min\{e_{\mathrm s},e_{\mathrm m}\}$ with $e_{\mathrm s}$ and $e_{\mathrm m}$ representing the probe and measurement logarithmic entanglement negativities, respectively. Maximally entangled probes and SWAP measurements reduce this cost to a constant number of queries. Furthermore, we develop a time-reversal symmetry test for arbitrary fixed, compatible probes and measurements, relate its query complexity to their logarithmic negativities, and match the lower-bound scaling in the high-entanglement regime by optimizing the probe and measurement. Our results establish a quantitative connection between entanglement and time-reversal symmetry, bridging two central concepts in quantum information science and fundamental physics.
Comments40 pages, 2 figures
