Based on your question, doing a "quick erase" only erases the tape header information and not the entire tape data information. A "full erase" erases both. However, if you concerned about your data being accessed off this tape, your best solution is to have the tape degaussed by a reputable service. Look for a tape degausser that has a coercivity value of 2-3 times that of the tape you are degaussing. Hope this helps.
