How much entanglement can be created in a closed system?
arXiv:1906.04234 · doi:10.1103/PhysRevB.101.060401
Abstract
In a closed system, the total number of particles is fixed. We ask how much does this conservation law restrict the amount of entanglement that can be created. We derive a tight upper bound on the bipartite entanglement entropy in closed systems, and find what a maximally entangled state looks like in such a system. Finally, we illustrate numerically on an isolated system of one-dimensional fermionic gas, that the upper bound can be reached during its unitary evolution, when starting in a pure state that emulates a thermal state with high enough temperature. These results are in accordance with current experiments measuring Rényi-2 entanglement entropy, all of which employ a particle-conserving Hamiltonian, where our bound acts as a loose bound, and will become especially important for bounding the amount of entanglement that can be spontaneously created, once a direct measurement of entanglement entropy becomes feasible.
arXiv comment5 pages, 4 figures. v2: extended numerical simulations, now including cases with no interaction and no hopping, extended discussion, added evaluation of the bound in the thermodynamic limit
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