What I've found that works best for me is being gentle with my skin and maintaining the same anti-acne routine.
I tried tumeric once, and it stains your skin. My entire face was yellow. It stained my nails yellow. The sink, everything. I had to scrub and scrub and scrub to get it off. The scurbbing made my skin very irritated and red-- something that makes my marks stand out more. It was a bad experience.
I make a mask using plain yogurt, honey, and some lemon juice. It does a pretty good job of brightening marks. But with most hyperpigmentation and acne treatments, don't expect miracles.
Edit: I forgot to mention, there have been studies that link benzoyl peroxide to making post acne marks harder to fade. Sal acid would probably be better.
Also, use sunscreen. The sun can make hyperpigmentation marks darker and thus make them take longer to fade.
It's worth noting that if you exfoliate your skin a lot, some form of sun protection is needed, because of the new layers of skin being exposed. The sun also darkens some peoples red marks, making them last longer.