The simple answer is no, you cannot dive alone as a PADI Open Water diver.
However the PADI Self Reliant Diver course teaches you to learn self reliance either whilst diving with a buddy or alone. The course is ideal for divers with a passion for photography or videography. The prerequisite for this course is a minimum of Advanced Open Water certified with no less than 100 logged dives. To qualify you must also complete a dive skills assessment.