Complexity of frustration: A new source of non-local non-stabilizerness
Complexity of frustration: A new source of non-local non-stabilizerness
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DOI：
10.21468/scipostphys.15.4.131
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发表时间：
2022-09
期刊：
影响因子：
5.5
通讯作者：
Jovan Odavić;Tobias Haug;G. Torre;A. Hamma;Fabio Franchini;S. Giampaolo
中科院分区：
文献类型：
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作者：
Jovan Odavić;Tobias Haug;G. Torre;A. Hamma;Fabio Franchini;S. Giampaolo
我们通过检查嵌入自旋链中的 WW 状态来推进量子多体系统复杂性的表征。这些状态显示出一定程度的非稳定性或“魔力”，以稳定器 Rényi 熵来衡量，它随着量子位/自旋的数量呈对数增长。我们关注的是哈密顿量承认具有广泛简并性的经典点的系统。在这些点附近，克利福德电路可以将基态转换为 WW 态，而在经典点所属的相位的其余部分，它具有局部量子相关性。拓扑受阻量子自旋链主相具有所需的现象学，我们表明它们的基态稳定器 Rényi 熵是 WW 状态的稳定器 Rényi 熵加上广泛的局部贡献的总和。我们的工作表明，WW 态/受挫基态表现出非局域的复杂性，可以作为量子资源获取，并且在 GHZ 态/非受挫系统中没有对应物。
We advance the characterization of complexity in quantum many-body systems by examining WW-states embedded in a spin chain. Such states show an amount of non-stabilizerness or “magic”, measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a WW-state, while in the rest of the phase to which the classical point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state’s Stabilizer Rényi Entropy is the sum of that of the WW-states plus an extensive local contribution. Our work reveals that WW-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.