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 acting on random factorized states by a circuit of length 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 , 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 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 the reduced state becomes very close to the completely mixed state.
- Received 30 September 2011
- Corrected 27 July 2012
DOI:https://doi.org/10.1103/PhysRevLett.109.040502
© 2012 American Physical Society
Corrections
27 July 2012