To what extent do parents have the right to "spy" on their children?

Polonius is spying on Ophelia and Hamlet. Polonius is Ophelia's father and thinks that Hamlet and Ophelia have a relationship going on. In this case, I think that her parents should be spying on Ophelia because she hasnt been being truthful. She hasnt told her dad that she likes Hamlet, so her dad had to improvise. And I think that it is completely okay that he is spying on his daughter, because I think that all children should tell there parents the truth. So that when there parents decided to spy on them, they will have nothing new to find out.
However I dont think that parents need to spy all the time. There needs to be a bond between the parents and the children that should be built when they are little. Therefore, parents need to have some trust in there kids. And the way they raised there children. Therefore, I think that it is highly dependant on the child and how honest the kid is.
But i think that children have too much free time to surf the web and research something that should be supervised. I know that some kids have got caught looking up naughty things on the internet or watching bad movies and when parents look at those type of things I think it is completely okay. The only time when I dont think that a parent should be spying is when there child has done nothing to make them not trust them. I truely believe that everyone is innocent til proven guilty.