Can you share (maybe thru DM if its a private matter) a bit of the background ?
Are you a freelancer, or a tech / BPO startup , or a young organization ?
Employees perform better when they are in a environment where they are encouraged to perform better.
You can identify a good co-working place which has CCTV if you are concerned about their moving around while on office hours.
You can also request the employee to update the logbook for in & out timings at Begin and end of day.
In fact some office space providers give you Employee IDs with tracking.
If possible avail of a VPN service to keep employees on your network and prevent them from accessing unwanted sites via proxies.
Anything beyond that like logging software can amount to unnecessary employee surveillance which can kill productivity and trust between you and your employees.
If the employee in question would like to avail of Work From Home facility , ask them to work at least an hour or two extra on a daily basis and tell them to keep a log book to record daily productivity.
In fact you can create the excel sheet in google docs with tasks and time columns for them and ask them to update it in real time.
Also have a weekly / fortnightly IN PERSON review meeting to see if the WFH facility is productive for your organization.