Nanobots would be the least efficient method of converting Mars' atmosphere.
Nanobots are not a magic wand solution. They need energy to operate. If they can't be constantly receiving energy they need to store the energy. The problem is that they are very small so their storage capacity would be small. Now, nanobots could form networks to transmit energy from where it is generated (assuming a nuclear reactor) to where it is needed. The trouble is that almost all nanobots would be used maintaining their infrastructure.
Here are your energy needs:
- So, you would need the energy to do the job of freeing oxygen and
nitrogen (~80% of Earth's atmosphere).
- You would also need the energy to operate all of the nanobots that
get that energy from where you make it to where you need it.
- You also need energy to make new nanobots as, being small, they
break easily. Think of how many skin cells a human sheds.
- You need energy to control the nanobots. They are too small to have
much thinking capacity. Each new task needs to be programmed in to
each bot (assuming they are programmable at all). So, you need a lot of computing power and bandwidth for transmission.
- You need energy to find and mine the materials to build more nanobots (they
generally aren't made out of common materials).
As you can see here, the only thing that using nanobots would give you is flexibility. Nanobots simply make a self configurable machine general purpose. Any general purpose tool will be less efficient at its job than a tool designed to do that job.
The one thing that nanobots could be used for is to build the tunnels and cabling (and, maybe, the machinery) needed to do the job. In this case they would operate like ants but then leave leave behind efficient tools that do the actual job.
The trouble that I have with using nanobots is that if you have the tech to make efficient nanobots (quantum entangled communication and energy transmission), you have the tech to do it without the nanobots. It is like making a Rube Goldberg device to flip a light switch. It might be cool to do but while you are messing with that, I'll have walked over, flipped the switch on, finished reading my book, flipped the switch off, and gone home.
Just throw 4-5 comets at Mars (that'll melt some ice) and come back in 150 years when it's cooled off a bit.