Superdense Coding

Imagine you need to send classical information through a quantum channel that can only transmit one qubit at a time. How much information can you send?

Classical approach using qubits:

• Send $|0\rangle$ to represent bit $0$
• Send $|1\rangle$ to represent bit $1$
• Result: 1 qubit carries 1 bit of information

But quantum mechanics allows something remarkable: if Alice and Bob share entanglement beforehand, Alice can send 2 classical bits by transmitting just 1 qubit!

The setup:

1. Pre-shared entanglement: Alice and Bob share a Bell state $|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$
2. Alice has: First qubit of the Bell pair
3. Bob has: Second qubit of the Bell pair
4. Goal: Alice sends 2 classical bits by transmitting her 1 qubit to Bob

Why this matters:

• Channel capacity: Double the classical information through quantum channels

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