Lecture Playlist

Introduction to quantum mechanics

The basic logic of quantum mechanics

Vector spaces and operators

Time evolution of a quantum system

Uncertainty, unitary evolution, and the Schrödinger equation

Entanglement

Entanglement and the nature of reality

Particles moving in one dimension and their operators

Fourier analysis applied to quantum mechanics and the uncertainty principle

The uncertainty principle and classical analogs
This lecture takes a deeper look at entanglement. Professor Susskind begins by discussing the wave function, which is the inner product of the system's state vector with the set of basis vectors, and how it contains probability amplitudes for the various states. He relates these probability amplitudes to the expectation values of observables discussed in previous lectures.
He then examines more deeply the difference between product and entangled states. For product states, the wave function factorises which allows the two (or more) subsystems to be treated as independent systems. He also describes the properties of a maximally entangled two spin system, and introduces the concept of density matrices, which express everything we can know about one part of an entangled system.
Professor Susskind then moves on to discuss measurement versus entanglement. There are two views of measurement: one in which the measuring apparatus becomes entangled with the system under measurement, and the other in which the wave function of the system under measurement collapses when measured.
He then discusses locality beginning with Einstein's famously skeptical phrase "spooky actions at a distance." He distinguishes between actual instantaneous action at a distance  which is impossible  and simple correlation. What is strange about quantum mechanics is not correlation in entangled states, but rather that we can know everything about this system as a whole, without knowing anything about the individual states of the entangled elements.
Professor Susskind concludes the lecture by revisiting the example of the computer simulation from the last lecture, which is an example of Bell's theorem that local hidden variables are not sufficient to explain quantum mechanics.
 Quantum wave function
 Product vs. entangled states
 Singlet state
 Maximum entanglement
 Density matrices
 Measurement
 Locality
 Spooky action at a distance
 Computer simulation of product and entangled states
 Bell's theorem
 Hidden variables