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Superdense Coding

Overview

Superdense Coding is a quantum communication protocol that allows a sender (Alice) to send two classical bits of information to a receiver (Bob) by transmitting only a single qubit. This protocol demonstrates the power of pre-shared quantum entanglement as a resource.

For the protocol to work, Alice and Bob must initially share an entangled pair of qubits (a Bell pair).

Technical Circuit Logic

The protocol involves 2 qubits and the following stages:

  1. Entanglement Sharing: Alice and Bob share a Bell pair $|\Phi^+\rangle = \frac{|00\rangle + |11\rangle}{\sqrt{2}}$. Alice holds qubit $q_0$ and Bob holds qubit $q_1$.
  2. Alice's Encoding: Alice wants to send a 2-bit message $m_1 m_0$. She applies local gates to her qubit $q_0$:
    • To send 00: Apply $I$ (do nothing).
    • To send 01: Apply $Z$ gate.
    • To send 10: Apply $X$ gate.
    • To send 11: Apply $X$ and $Z$ gates.
  3. Transmission: Alice sends her qubit $q_0$ to Bob.
  4. Bob's Decoding: Bob now has both qubits. He performs a Bell basis measurement by reversing the entanglement steps:
    • Apply CNOT($q_0, q_1$).
    • Apply $H(q_0)$.
    • Measure both qubits. The result $q_1 q_0$ corresponds exactly to the 2-bit message Alice intended to send.

API Reference

The module src.algorithms.superdense_coding provides functions to demonstrate the protocol.

create_superdense_circuit(message: str) -> QuantumCircuit

Constructs a 2-qubit circuit that encodes a 2-bit classical message into a shared Bell pair.

  • Args: message (str) - One of '00', '01', '10', or '11'.
  • Returns: A qiskit.QuantumCircuit implementing the encoding and decoding.

run_simulation(qc: QuantumCircuit, message: str) -> Dict[str, int]

Simulates the circuit locally and generates visual outputs.

  • Side Effects:
    • Saves the circuit diagram to outputs/superdense_circuit_<message>.png.
    • Saves the result histogram to outputs/superdense_histogram_<message>.png.
  • Returns: A dictionary of measurement counts.

Usage Example

from src.algorithms.superdense_coding import create_superdense_circuit, run_simulation

# Send the message '10'
msg = '10'
qc = create_superdense_circuit(msg)

# Run and visualize
counts = run_simulation(qc, msg)

print(f"Original Message: {msg}")
print(f"Decoded Message: {counts}")
# Expected output: {'10': 1024}

Implementation Details