Journal
PHYSICAL REVIEW LETTERS
Volume 109, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.109.040502
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Funding
- Government of Canada through NSERC
- Province of Ontario through MRI
- NSF [PHY-803304, PHY-0969969]
- ARO MURI [W911NF-11-1-0268]
- Division Of Physics
- Direct For Mathematical & Physical Scien [803304] Funding Source: National Science Foundation
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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.
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