February 13, 2012

Professor Susskind begins the lecture with a review of the problem of a single spin in a magnetic field. He re-emphasizes that observables corresponding to the Pauli sigma matrices do not commute, which implies that they obey the uncertainty relationship, and reviews the principles by which the spin in a magnetic field will radiate a photon and transition to the lowest possible energy state.

Professor Susskind then moves on to discuss the effect of measurement on a quantum system and the concept of wave function collapse. In general, the measuring apparatus becomes part of the quantum system and the space of states for the combines system is the tensor product of the states of the individual system components. This is the concept of entanglement.

Professor Susskind demonstrates the simplest example of entanglement of a two spin system. He distinguishes the unentangled product states from the more general entangled states, and gives examples or operators and expectation values for each. The singlet and triplet states are introduced.

Professor Susskind concludes the lecture by summarizing the essence of entanglement in the principle that, although a single spin quantum mechanical system can be simulated with a classical computer, a two spin system cannot be simulated by two classical computers unless they are connected together.

Topics: 
  • Wave function collapse
  • Tensor products
  • Product states
  • Entanglement
  • Observables for entangled states
  • Expectation values of entangled states
  • Singlet and triplet states