In my opinion you should have a password on your phone but your partner should know your password. The information on your phone is personal and you don’t want everyone to be able to access it. However, in a healthy relationship your partner should know your password. I believe, in an open and transparent relationship based on trust in which you share everything there are no secrets and there is nothing to hide. Therefore, there shouldn’t be a problem to share ones phone password with the partner. If the partner doesn’t want to share the password I would get a feeling that s/he has something to hide or something s/he doesn’t want you to see. This will cause misunderstanding which will harm the relationship. So -password -yes, but share it with your partner.