Fundamental error bound for entanglement generation between interacting Rydberg atoms

Abstract

We analytically derive the lower error bound for the preparation of any maximally entangled state of two atoms involving Rydberg-state interactions. This fundamental bound represents the minimum achievable error $E\ge (1+\pi /2)\Gamma /B$ due to spontaneous decay $\Gamma$ of the Rydberg states and their finite interaction strength $B$, assuming that all other technical errors can be eliminated. Using quantum optimal control methods, we identify laser pulses for preparing a maximally entangled state of a pair of atomic qubits with an error only $1\%$ above the derived fundamental bound.

9 pages, 2 figure