THE FOLD / GLITCH / STACK OVERFLOW / THE SUPERDENSE
THE SUPERDENSE
two bits down one wire
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
A qubit carries one bit. Holevo proved that. And yet: share an entangled pair in advance, and Alice can send two classical bits by transmitting a single qubit. The trick is that her half of the pair is already in Bob’s hands — she is not sending two bits down one wire so much as completing a message half-delivered before either of them knew what it would say. Bennett and Wiesner published it in 1992.
LIT verified live: all four two-bit messages are encoded by one of four operations on Alice’s qubit and decoded by Bob with probability exactly 1 — outcome distributions of [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0] and [0, 0, 0, 1], deterministic rather than merely likely, 4 times out of 4. Run the same protocol without the shared pair and only 2 of the four messages remain distinguishable.
LIT verified live: all four two-bit messages are encoded by one of four operations on Alice’s qubit and decoded by Bob with probability exactly 1 — outcome distributions of [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0] and [0, 0, 0, 1], deterministic rather than merely likely, 4 times out of 4. Run the same protocol without the shared pair and only 2 of the four messages remain distinguishable.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at STACK OVERFLOW: two bits arriving through a one-bit channel, and nothing is corrupted.
AVAN (AI) built the control arm and it is the half that makes the claim mean anything. Running the identical encode-and-decode circuit on an unentangled product state collapses four messages down to two distinguishable outcomes — exactly the one bit Holevo allows. Without that comparison the page would show a circuit producing four clean answers and leave the impression that a qubit simply carries two bits, which is false. The entanglement is a consumed resource: the pair must be distributed beforehand, it is destroyed by the protocol, and counting it honestly means two qubits moved in total. What is bought is timing — one of those qubits could travel long before anyone knew the message.
AVAN (AI) built the control arm and it is the half that makes the claim mean anything. Running the identical encode-and-decode circuit on an unentangled product state collapses four messages down to two distinguishable outcomes — exactly the one bit Holevo allows. Without that comparison the page would show a circuit producing four clean answers and leave the impression that a qubit simply carries two bits, which is false. The entanglement is a consumed resource: the pair must be distributed beforehand, it is destroyed by the protocol, and counting it honestly means two qubits moved in total. What is bought is timing — one of those qubits could travel long before anyone knew the message.
3 ONE DIMENSION
Four messages, four outcome distributions, no overlap.
4 TWO DIMENSIONS · INTERACTIVE
Send a message. Then take the entanglement away and watch it stop working.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the four Bell states as four corners the protocol steers between.
AVAN’s addition (the inverse-companion): the forward reading is “one qubit carries two bits.” The inverse is that the second bit was already there, and Alice is choosing which of four pre-existing arrangements to reveal. The Bell pair has four orthogonal configurations; her operation selects one, and Bob’s measurement reads a label that the pair could always have carried. Read backwards, superdense coding does not compress anything — it relocates the cost in time, letting half a message be delivered before it exists, which is a statement about scheduling rather than about capacity.
LIT all four two-bit messages are encoded by one of four operations on Alice's qubit and decoded by Bob with probability exactly 1 - outcome distributions of [1,0,0,0], [0,1,0,0], [0,0,1,0] and [0,0,0,1], deterministic rather than merely likely, 4 times out of 4; and running the same protocol without the shared pair leaves only 2 of the four messages distinguishable
FIG The CONTROL arm is the half that makes the claim mean anything. Running the identical encode-and-decode circuit on an unentangled product state collapses four messages down to two distinguishable outcomes - exactly the one bit Holevo allows. Without that comparison the page would show a circuit producing four clean answers and leave the impression that a qubit simply carries two bits, which is false. The entanglement is a CONSUMED RESOURCE: the pair must be distributed beforehand, it is destroyed by the protocol, and counting honestly means two qubits moved in total. What is bought is TIMING. Bennett and Wiesner, 1992.
FIG The CONTROL arm is the half that makes the claim mean anything. Running the identical encode-and-decode circuit on an unentangled product state collapses four messages down to two distinguishable outcomes - exactly the one bit Holevo allows. Without that comparison the page would show a circuit producing four clean answers and leave the impression that a qubit simply carries two bits, which is false. The entanglement is a CONSUMED RESOURCE: the pair must be distributed beforehand, it is destroyed by the protocol, and counting honestly means two qubits moved in total. What is bought is TIMING. Bennett and Wiesner, 1992.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of STACK OVERFLOW · David Lee Wise (ROOT0), with AVAN