Optimal Entangling Capacity of Dynamical Processes

Abstract

We investigate the entangling capacity of dynamical operations when provided with local ancilla. A comparison is made between the entangling capacity with and without the assistance of prior entanglement. An analytic solution is found for the log-negativity entangling capacity of two-qubit gates, which equals the entanglement of the Choi matrix isomorphic to the unitary operator. Surprisingly, the availability of prior entanglement does not affect this result; a property we call resource independence of the entangling capacity. We prove several useful upper-bounds on the entangling capacity that hold for general qudit dynamical operations, and for a whole family of entanglement monotones including log-negativity and log-robustness. The log-robustness entangling capacity is shown to be resource independent for general dynamics. We provide numerical results supporting a conjecture that the log-negativity entangling capacity is resource independence for all two-qudit unitaries.Comment: Changed title since previous version. 8 pages main text + 4 pages of appendices. Rewritten with some mathematical details moved to appendices. Accepted for publication in Physical Review