Learning objectives
By the end of this lesson, you should be able to:
- Recognize a Bell state.
- Explain why an entangled state cannot be factored into independent qubits.
- Interpret correlated measurement statistics without implying faster-than-light signaling.
Prerequisites: Quantum Superposition·Tensor-product intuition
EXPERIMENT Interactive quantum laboratory
Change → Observe → ExplainManipulate the controls. Do not just watch the animation—predict what should happen before moving each parameter.
A two-qubit state that does not factor
One of the four Bell states is
\[|\Phi^+\rangle=\frac{|00\rangle+|11\rangle}{\sqrt2}.\]
This state cannot be written as a tensor product of an independent state for qubit A and an independent state for qubit B. The pair must be described as a joint quantum state.
Correlated measurements
When both qubits are measured in the computational basis, the outcomes 00 and 11 each occur with probability one half, while 01 and 10 do not occur ideally. Use the simulator to see the correlations over individual and repeated measurements.
Entanglement creates correlations stronger than those available from a simple product state, but it does not enable controllable faster-than-light communication.
Key takeaways
What should stay with you
- Entanglement is a property of the joint state.
- Bell-pair measurements are correlated.
- Correlation alone is not a mechanism for superluminal communication.
Knowledge check
For |Φ⁺⟩=(|00⟩+|11⟩)/√2, which ideal computational-basis outcomes can occur?
The Bell state has nonzero amplitudes only for |00⟩ and |11⟩, each with probability 1/2.