Optimal Entangling Capacity of Dynamical Processes

TL;DR

This paper analyzes the maximum entanglement generation of quantum operations, revealing that prior entanglement does not enhance this capacity for certain measures and providing bounds and conjectures for general cases.

Contribution

It derives an analytic expression for the log-negativity entangling capacity of two-qubit gates and establishes resource independence of this capacity, supported by bounds and numerical evidence.

Findings

Log-negativity entangling capacity equals the entanglement of the Choi matrix.

Prior entanglement does not increase the entangling capacity for the measures studied.

Numerical results support resource independence conjecture for all two-qudit unitaries.

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.