Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength

Understand

Entanglement properties of bipartite unitary operators are studied via their local invariants, namely the entangling power $e_p$ and a complementary quantity, the gate typicality $g_t$.

• We characterize the boundaries of the set $K_2$ representing all two-qubit gates projected onto the plane $(e_p, g_t)$ showing that the fractional powers of the \textsc{swap} operator form a parabolic boundary of $K_2$, while the other bounds are formed by two straight lines.
• In this way a family of gates with extreme properties is identified and analyzed.
• We also show that the parabolic curve representing powers of \textsc{swap} persists in the set $K_N$, for gates of higher dimensions ($N>2$).