Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

Randomness Changes Everything - The Algebra of Mixed Quantum States

Audience:

Tags: quantum-mechanics

Strange things start happening when you mix quantum theory with classical probability. Entirely different looking descriptions turn out to be physically indistinguishable, and it is impossible to say whether the randomness of measurement outcomes is due to quantum superposition or classical uncertainty. The two cannot be separated. Are they even different things at all? The standard wavefunction description can be misleading. Density matrices and the algebraic approach, which I discuss here, handle this much better. This is aimed at an audience with some knowledge of quantum mechanics, most likely at an undergraduate or graduate level. However, it should be accessible to anyone with an interest in the subject.


Analytics

5.45 Overall score*
96 Rank
11 Votes
6 Comments

Comments

5.1

The way it was explained was good, but too much equations are present in the lecture

5

The video starts with a good example by demonstrating how quantum cryptography can be used to determine if there were spies trying to attain information, but after that it gets lost in the symbolic manipulation. This video seems like it starts off catering to all audiences, but I would assume most people would start to lose interest around the 10 minute mark. The ideas presented are interesting, like how the symbolic manipulation reveals how spin up and spin down cannot be distinguished from spin right and spin left, but the script could use some reworking to cater to the right audience.

3

I know nothing about quantum mechanics and this video is too greedy I think … It tries to explain a lot of concepts in one shot … In my opinion it didn’t make a good job with such ambitious goal in mind and may be the target audience must be the people that already had some knowledge about phisics and/or quantum mechanics… The speaker also talked as he was in a place where he was invited to give a kind of master class with very technical terms without explaining them for the general public… That isn’t the spirit of the SoME presentations… Even though the video is well done in general… I couldn’t watch the entire video because it wasn’t for me …

7.4

kinda leaves you with more questions than you’ve came with, but in a good, thought provoking, way.

5

I enjoyed how you introduced these interesting and curious questions, so that hooked me into watching further. Overall, there is a lot of broad material contained in this video. Maybe try breaking down some more concepts for every 10 minute interval of the video (the std ways to see it in quantum then classical). Your Ranking score was determined by these individual scores per each criteria: Motivation: 9 Clarity: 5 Novelty: 3 Memorability: 3

7.8

I have recently studied this topic with a book, so I can’t assess whether everything is clear to a newcomer. I do think the video includes all the ingredients relevant to the topic and works well for people at different levels of quantum mechanics. To me, the point of equivalence of states got hammered in a bit too much. The section on density matrices themselves could have been a bit longer, also including a concrete example, e.g. where you only showed the general matrix for a single q-bit.