This video was my winning entry for the 2017 CCIMI Video Contest (https://www.ccimi.maths.cam.ac.uk/ccimi-video-contest/). Many thanks to falcxne for allowing use of his songs "Said You Wouldn't Change" (from the album Timbits III), "I Hate Homework (Interlude)" (from Timbits II) and "NYC (Interlude)" (from Timbits III); you can find these and more at https://falcxne.bandcamp.com/. And thanks to Phillipe Faist for creating the entropy zoo, which you can find here: https://www.its.caltech.edu/~phfaist/.... For more details on the continuity bounds mentioned, you can find a preprint here: https://arxiv.org/abs/1707.04249, which is joint work with my supervisor, Dr. Nilanjana Datta.
Lastly, one clarification: in the video, I talk about the data-compression example in the language of classical information theory, for simplicity. However, the quantum case can be described in a very similar way, with the von Neumann entropy replacing the Shannon entropy.