What are some current algorithm(s) for finding if two images are copies of each other?
This is not a simple problem. You need to define these 'simple edits' and check for all of those. 

For example if you want to find out brightness changes, you cannot effectively use template matching, you would have to go with feature matching (contour, keypoint etc.).

For a general solution, you need to extract a 'signature' from an image which for instance can be done with a combination of histogram and feature points (edge, corner, blob, Shi-Tomasi, LoG etc.)