QUANTUM 05
Building entanglement with H and CNOT, and why it matters for security
Sinclair College - Dr. Mike Libassi
TODAY
01 · ENTANGLEMENT
An entangled state can't be written as "qubit A is this, and qubit B is that." Only the pair has a well-defined state.
|0⟩ ⊗ |+⟩. Each qubit has its own state, so the pair can be split.
1/√2 (|00⟩ + |11⟩). No way to split it into two separate qubits.
Measure one qubit and you instantly know the other's result.
02 · THE CIRCUIT
|00⟩: both qubits at 0
1/√2 (|00⟩ + |10⟩): q0 in superposition
q0 controls q1: flips q1 only in the |1⟩ branch
|Φ⁺⟩ = 1/√2 (|00⟩ + |11⟩)
Only |00⟩ and |11⟩ remain. Whichever result one qubit gives, the other matches it.
02 · THE CIRCUIT
| Input | Bell state | Both measure Z | Both measure X |
|---|---|---|---|
| |00⟩ | |Φ⁺⟩ = 1/√2 (|00⟩ + |11⟩) | always match | always match |
| |01⟩ | |Ψ⁺⟩ = 1/√2 (|01⟩ + |10⟩) | always differ | always match |
| |10⟩ | |Φ⁻⟩ = 1/√2 (|00⟩ − |11⟩) | always match | always differ |
| |11⟩ | |Ψ⁻⟩ = 1/√2 (|01⟩ − |10⟩) | always differ | always differ |
03 · MEASURING PAIRS
Alice's results look like fair coin flips. So do Bob's.
Compared side by side, their results are perfectly correlated.
The correlation vanishes. Results look unrelated.
03 · MEASURING PAIRS
Entanglement is correlation, not communication.
04 · SECURITY
A source sends Bell pairs to Alice and Bob; matching-basis results become key bits.
An eavesdropper breaks the entanglement, weakening correlations in a testable way.
Entanglement is the resource behind quantum repeaters and future quantum internet links.
WRAP-UP
Entangled states can't be split into separate qubit states
H then CNOT turns |00⟩ into the Bell state |Φ⁺⟩
Each result is random, but the pair is perfectly correlated
Entanglement enables E91 key distribution but no FTL messaging
DISCUSSION
If each person's entangled results are random, what makes them useful for building a shared key?
Think about what Alice and Bob each end up holding, and what an eavesdropper doesn't.