Even if we had a means of producing anitmatter in quantity and advanced storage bottles for it, propellent would still be required. Hydrogen is the most efficient for propulsion, but it's easier and more reliable to use water.
This kind of system could be used first to transport equipment and provisions before humans make the trip and give us opportunities to work out any bugs and be sure it's safe enough for human travel. And such test/supply vehicles left in Mars orbit could serve as a supply of propellent and spare parts for any return trips.
And no, water is not a chemical fuel in this context, just propellent.
I looked at the Wikipedia article cited above before posting, but what I'm proposing not quite the same. I'm saying build something big, simple, cheap, and ugly that makes the trip fast enough to minimize negative effects on human health and able to maintain artificial gravity on the way. Having to carry conventional fuel means needing more fuel just to transport the fuel. I say let sunshine be your fuel. It just takes a huge mirror to grab enough of it to get the job done.
It could be done going back and forth to the moon first just to get used to this method and improve the engineering details before taking a crack at Mars.