I. the Differences between Quantum and Classical States

Now that you have learned the basic quantum formalism from an axiomatic point of view and are skilled in manipulating the mathematical objects we need, I want to loop back and ask what exactly the quantities you have been manipulating mean. You’ve probably heard that there are some “weird” aspects to quantum mechanics and its historically been somewhat of a nonintuitive theory. Maybe you have already run into some of this weirdness in the first few weeks of this course. In this lecture I want to dig into this further and give you some more details about what exactly it is that makes quantum theory weird. This is not only important for understanding the foundations of the subject, but some of the things we identify as being “quantum weirdness” in this lecture are exactly what will be exploited as features in quantum information applications. I should say that what I’m going to do is a little unfair. I’m going to try to condense a century of some of the deepest thinking in physics and philosophy into one lecture. Unfortunately this means that we’ll have to skip over some subtleties, but hopefully this will give you a flavor of the main ideas (and there is further reading material listed at the end).