纠缠与非局域非稳定性的通用预算
A Universal Budget for Entanglement and Nonlocal Non-Stabilizerness
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中文总结 AI 辅助
该研究为二分纯态中纠缠与非局域非稳定性的同时分配建立了通用二次约束，并揭示其不对称性，为张量网络截断提供资源感知控制依据。
中文摘要 AI 辅助
纠缠和非局域非稳定性是编码在二分纯态的施密特谱中的两种不同的量子资源。对于量子比特系统，我们建立了它们同时分配时的通用二次约束，该约束由每侧编码占据的施密特支撑所需的最小逻辑量子比特数决定。额外的谱约束揭示了它们分配中的强烈不对称性：纠缠可以耗尽逻辑容量，而最大非局域非稳定性仅随其对数增长。对于由单个分离虚拟边穿越的张量网络割，逻辑容量由占据的键维数决定。我们进一步从保留的施密特谱及其丢弃权重推导出未截断态资源的一侧证书。对于小的丢弃权重，由此产生的修正与该权重成线性关系。这些结果将通用资源预算与张量网络截断的资源感知控制联系起来。
英文摘要
Entanglement and nonlocal non-stabilizerness are distinct quantum resources encoded in the Schmidt spectrum of a bipartite pure state. For qubit systems, we establish a universal quadratic constraint on their simultaneous allocation, governed by the minimum number of logical qubits required on each side to encode the occupied Schmidt support. Additional spectral constraints reveal a strong asymmetry in their allocation with the Entanglement that can exhaust the logical capacity, whereas the maximal nonlocal non-stabilizerness grows only logarithmically with it. For a tensor-network cut crossed by a single separating virtual edge, the logical capacity is determined by the occupied bond dimension. We further derive a one-sided certificate for the resources of the untruncated state from a retained Schmidt spectrum and its discarded weight. For small discarded weight, the resulting corrections are linear in that weight. These results connect a universal resource budget to resource-aware control of tensor-network truncations.
发表机构
- Institut Ruđer Bošković（鲁杰尔·博什科维奇研究所）
机构由 AI 辅助整理，请以论文原文为准。
