I'm gonna say you can log it, but only under certain circumstances...
It requires a type rating to log PIC because it is a jet. Therefore, you may never log it as PIC unless you have that type rating.
If the airplane is operated under part 91 rules, you may log SIC.
If the airplane is operated under part 135 op specs, you may not.
If it's under 135 op specs, but you are flying an empty part 91 leg, then I'm not sure. You'd probably have to get an airline ticket just to get to the airplane to fly an empty leg anyhow, so it wouldn't be worth it.