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• W2080247779 abstract "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 by 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 {em in 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." @default.
• W2080247779 created "2016-06-24" @default.
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• W2080247779 date "2012-07-26" @default.
• W2080247779 modified "2023-10-11" @default.
• W2080247779 title "Quantum Entanglement in Random Physical States" @default.
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• W2080247779 doi "https://doi.org/10.1103/physrevlett.109.040502" @default.
• W2080247779 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/23006070" @default.
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