11.2 Superdense Coding

Superdense coding is a quantum communication protocol that transmits two classical bits using one qubit. It leverages quantum entanglement to double the classical information capacity of a quantum channel, offering advantages in efficiency and security over classical communication.

The protocol involves entanglement distribution, encoding by the sender (Alice), and decoding by the receiver (Bob). Alice applies specific unitary operations to her qubit based on the 2-bit message, while Bob performs a joint measurement to decode the information.

Superdense Coding Fundamentals

Definition of superdense coding

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• Superdense coding employs quantum communication protocol to transmit two classical bits of information using only one qubit
• Advantages over classical communication double the classical information capacity of a quantum channel by utilizing quantum entanglement to enhance communication efficiency
• Provides secure communication due to quantum properties such as no-cloning theorem and quantum measurement disturbance

Entanglement in superdense coding

• Quantum entanglement serves as fundamental resource in superdense coding creating non-classical correlations between two qubits (electron spin, photon polarization)
• Bell states represent maximally entangled two-qubit states used in superdense coding
• Four Bell states $|\Phi^+\rangle$, $|\Phi^-\rangle$, $|\Psi^+\rangle$, $|\Psi^-\rangle$ form basis for encoding and decoding information
• Entanglement distribution involves sending one qubit of the entangled pair to sender (Alice) and other qubit to receiver (Bob) establishing quantum channel

Superdense Coding Protocol

Processes of superdense coding

• Encoding process (Alice):
  1. Decides on 2-bit message to send (00, 01, 10, or 11)
  2. Applies corresponding unitary operation to her qubit:
     • I (identity) for 00
     • X (bit flip) for 01
     • Z (phase flip) for 10
     • XZ (bit and phase flip) for 11
  3. Sends modified qubit to Bob through quantum channel
• Decoding process (Bob):
  1. Receives Alice's qubit
  2. Performs joint measurement on both qubits using Bell state measurement (BSM)
  3. Distinguishes between four Bell states based on measurement outcome
  4. Determines original 2-bit message from measurement result

Superdense coding vs quantum teleportation

• Similarities utilize quantum entanglement as resource and involve transmission of quantum information
• Both require classical communication channels for complete protocol execution
• Differences:
  • Information flow: Superdense coding converts classical to quantum while quantum teleportation goes from quantum to classical to quantum
  • Resource requirements: Superdense coding uses one entangled pair and one qubit transmission whereas quantum teleportation needs one entangled pair and two classical bit transmissions
  • Applications: Superdense coding enables efficient classical information transfer while quantum teleportation allows transfer of unknown quantum states