Superdense Coding
Superdense coding sends two classical bits by transmitting one qubit, using a pre-shared entangled pair.
Two bits from one qubit
Superdense coding is the counterpart to teleportation. It lets Alice send two classical bits to Bob by physically transmitting only one qubit, provided they share an entangled pair in advance. It shows entanglement can double the classical capacity of a quantum channel.
The protocol
- Alice and Bob share a Bell pair |Phi+> = (|00>+|11>)/sqrt(2)
- Alice encodes two bits by applying one of I, X, Z, or ZX to her qubit
- This rotates the shared pair into one of the four Bell states
- Alice sends her single qubit to Bob
- Bob performs a Bell measurement on both qubits and reads off the two bits
Why it works
The four Pauli operations {I, X, Z, ZX} map |Phi+> to the four distinct, mutually orthogonal Bell states. Because they are orthogonal, a Bell measurement distinguishes them perfectly, recovering the two-bit message. Alice manipulated the global entangled state by acting only on her half.
Accounting the resources
Superdense coding does not violate Holevo's bound, which limits a lone qubit to one bit of retrievable information. The second bit is paid for by the pre-shared entanglement — a resource distributed earlier. In total, one qubit sent plus one ebit of shared entanglement conveys two classical bits, consistent with the accounting.
Duality with teleportation
Teleportation uses one ebit and two classical bits to send one qubit; superdense coding uses one ebit and one qubit to send two classical bits. They are mirror images, and together they illustrate how quantum and classical information can be traded against each other through entanglement.