Entanglement
Entanglement occurs when the state of a composite quantum system cannot be written as a simple product of states for its parts.
A product state looks like
An entangled state does not factor that way. A standard two-qubit example is
Neither subsystem has its own complete pure-state description, even though the combined state is sharply specified.
Why it matters
Susskind and Friedman stress entanglement as one of the features that makes quantum mechanics unlike classical physics. It turns “state of the whole” into something richer than “state of each part pasted together.”
What it does and does not imply
Entanglement creates correlations that can violate classical Bell-type expectations. It does not allow faster-than-light messaging by itself, because local outcomes are still individually random.
Common pitfalls
- Correlation alone is not necessarily entanglement; classical variables can be correlated too.
- Entanglement is basis-independent as a property of factorisation, although its expression changes with basis.
- Measuring one subsystem updates the joint-state description; it is not a usable superluminal signal.
Links: Hilbert space, Observable, Uncertainty principle. Source trail: Susskind The Theoretical Minimum index; reference book: Quantum Mechanics: The Theoretical Minimum by Leonard Susskind and Art Friedman.