Level 5 · Advanced undergraduate
Objective. Distinguish entanglement from classical correlation.
Before this lesson. L5-01, L3-04
Hands-on lab. Entanglement and Bell tests
Learn¶
A joint system uses a tensor product of component spaces. Two qubits have four computational basis states. A product state separates into one state for each qubit. An entangled pure state cannot be written as such a product.
The Bell state (|00> + |11>)/sqrt(2) gives equal local outcomes in the computational basis. A classical mixture of |00> and |11> gives the same outcomes in that basis. A second measurement basis is needed to distinguish these preparations.
Entanglement concerns the joint state, rather than any single correlation table. Local outcomes can remain random while joint outcomes show strong structure. This structure does not permit a controllable message faster than light. Compare complete experimental assumptions before interpreting a Bell test.
Practice¶
Solution
Each of the four X-basis pairs has probability 1/4. Two pairs have equal signs. Their combined probability is 1/2, unlike the Bell state value of one.
Check your understanding¶
Does perfect correlation in one basis prove entanglement?
A. Yes, in every case
B. No, a classical mixture can match it
C. Only with more repeated trials in that basis
Show the answer
B. No, a classical mixture can match it
A separable classical mixture can give the same single-basis correlation. Additional measurement settings are needed to exclude that explanation.
Sources¶
This lesson draws on Watrous, 2018Preskill, n.d..
Next: L5-05 · Density operators and reduced states
- Watrous, J. (2018). The Theory of Quantum Information. https://cs.uwaterloo.ca/~watrous/TQI/
- Preskill, J. (n.d.). Course Information for Physics 219/Computer Science 219 Quantum Computation (Formerly Physics 229). California Institute of Technology course page with lecture notes. https://www.preskill.caltech.edu/ph219/