Quantum entanglement in random physical states.
Quantum entanglement in random physical states.
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DOI：
10.1103/physrevlett.109.040502
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发表时间：
2011-09
影响因子：
8.6
通讯作者：
A. Hamma;S. Santra;P. Zanardi
中科院分区：
文献类型：
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作者：
A. Hamma;S. Santra;P. Zanardi
希尔伯特空间中的大多数态都是最大纠缠的。事实证明，这一事实对研究统计力学的基础是有用的。不幸的是，量子多体系统的希尔伯特空间中的大多数态都是物理上不可访问的。我们定义了作用在随机因式分解态上的态的物理系综，定义了长度为k的具有局部支撑性的随机和独立么正元的回路。我们利用约化态的纯洁性来研究纠缠的典型性。我们发现，对于一个时间k=O(1)，典型的纯度服从面积定律。因此，平均而言，面积定律的上界实际上是饱和的，对于大系统来说，方差为零。类似地，我们证明了线性维子系统L在时间尺度上与体积定律的局域演化是典型的纠缠。此外，我们还表明，对于较大的k值，简并态变得非常接近完全混合态。
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate--among other things--the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many-body system are not physically accessible. We define physical ensembles of states acting on random factorized states by a circuit of length k of random and independent unitaries with local support. We study the typicality of entanglement by means of the purity of the reduced state. We find that for a time k=O(1), the typical purity obeys the area law. Thus, the upper bounds for area law are actually saturated, on average, with a variance that goes to zero for large systems. Similarly, we prove that by means of local evolution a subsystem of linear dimensions L is typically entangled with a volume law when the time scales with the size of the subsystem. Moreover, we show that for large values of k the reduced state becomes very close to the completely mixed state.