Bell State Experiment

Overview

This page demonstrates entanglement as an experiment you can run:

• create a Bell state with two qubits
• measure both qubits
• observe strong correlations that do not look like “independent coin flips”

Conceptual Mapping

In Foundations (entanglement section), you learned:

• an entangled state is not separable into “state of qubit A” times “state of qubit B”
• measurements can be correlated even when each qubit individually looks random

In Gates & Circuits, you learned a standard recipe:

• apply a Hadamard to create superposition
• apply a controlled gate to create entanglement

In code, that becomes:

• h(0) then cx(0, 1)
• measure both qubits and look at the joint bitstrings

Code Walkthrough

Create and measure a Bell state:

from qiskit import QuantumCircuit
from qiskit_aer import AerSimulator
 
qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure(0, 0)
qc.measure(1, 1)
 
sim = AerSimulator()
counts = sim.run(qc, shots=1000).result().get_counts()
print(counts)

Line by line:

• QuantumCircuit(2, 2) gives two qubits and two classical bits.
• h(0) puts qubit 0 into a superposition.
• cx(0, 1) “links” qubit 1 to qubit 0, creating an entangled pair.
• The two measure(...) calls record both outcomes.
• counts summarizes how often each two-bit result occurred.

Results & Interpretation

What you should typically see:

• mostly 00 and 11
• very little 01 or 10

Interpretation:

• each qubit alone looks random (0 or 1 can occur)
• but the pair is correlated: they tend to match

This is the “theory becomes data” moment:

• entanglement does not mean “mystical influence”
• it means the joint state has structure that shows up as correlations in repeated measurement statistics

Connection to amplitudes:

• the circuit creates amplitudes primarily on |00⟩ and |11⟩
• measurement probabilities come from those amplitudes
• repeated shots reveal that probability mass

Turtle Tip

Common Pitfalls

Quick Check

What’s Next

Next we’ll run a tiny Grover search as a toy example. You’ll see how an oracle and amplitude amplification show up as a shifted measurement distribution.