Lecture 6  The Theoretical Minimum  Summary and Q&A
TL;DR
This content explains the concept of entanglement in quantum systems and discusses how two spins can be entangled, leading to the phenomenon of nonlocal correlations between their measurements.
Questions & Answers
Q: How can two spins be entangled in a quantum system?
Two spins can be entangled when their states are correlated in a way that the state of one particle cannot be described independently of the other. This leads to the phenomenon of nonlocal correlations between measurements on the two particles.
Q: Can all states of a quantum system be described as product states?
No, not all states of a quantum system can be described as product states. Entangled states, such as the singlet state, cannot be written as a simple product of individual states for each spin.
Q: How can entangled states exhibit zero expectation values for individual spin components but nonzero expectation values for certain observable combinations?
Entangled states can have nonzero expectation values for observable combinations because the entanglement leads to correlations between the spins. While the expectation values of individual spin components may cancel each other out, the correlations between the spins still manifest in observable combinations.
Q: Does the concept of entanglement depend on the choice of basis?
No, the concept of entanglement does not depend on the choice of basis. Entanglement is an intrinsic property of the quantum system, regardless of how the states are represented.
Summary & Key Takeaways

The content discusses the concept of spin in quantum systems and how two spins can be entangled, resulting in correlated measurements.

Entanglement refers to the connection between two particles where the state of one particle cannot be described independently of the other.

Entangled states can have unique properties, such as zero expectation values for individual spin components but nonzero expectation values for certain observable combinations.

The example of a singlet state, where two spins are antialigned with each other, is provided as a highly entangled state.