Task status doesn't matter much: nothing can be delivered until the whole story is done.

If you want to track how much time is left on a story (overall) by having people fill in remaining time on tasks, then split tasks per person.

That said:

• Big tasks might be an indication your stories are too big. In this case, the best solution is to reduce the scope and size of stories, and if you reduce it enough tracking remaining time on tasks doesn't matter any more (they're either done or not).
• SCRUM encourages everyone to pick up what needs doing. If you are assigning tasks to persons (as opposed to roles), then you're potentially preventing yourself from delivering a story, even if developer is doing nothing - because QA is bottlenecked.

Task remaining time doesn't matter much: nothing can be delivered until the whole story is done.

If you want to track how much time is left on a story (overall) by having people fill in remaining time on tasks, then split tasks per person.

That said:

• Big tasks might be an indication your stories are too big. In this case, the best solution is to reduce the scope and size of stories, and if you reduce it enough tracking remaining time on tasks doesn't matter any more (they're either done or not - sum of estimate on non done tasks is granular enough).
• SCRUM encourages everyone to pick up what needs doing. If you are assigning tasks to persons (as opposed to roles), then you're potentially preventing yourself from delivering a story, even if developer is doing nothing - because QA is bottlenecked.