Quantum entanglement in random physical states

Details Quantum entanglement in random physical states Quantum entanglement in random physical states

2011-09-20

arxiv.org/abs/1109.4391v2

Physics

Quantum Physics

Scientific paper

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. This simulates an evolution for finite time k generated by a local (time-dependent) Hamiltonian. We apply group theoretic methods to study these statistical ensembles. In particular, 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, while for a time k \sim O(L) the purity obeys a volume law, with L the linear size of the system. Moreover, we show that for large values of k the reduced state becomes very close to the completely mixed state.

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