LOCC, Quantum Teleportation, and Repeaters
Stub. Local operations and classical communication (LOCC) as the standard restricted class of operations two (or more) distant parties sharing entanglement can perform — the right setting for asking what entanglement is good for; quantum teleportation, which uses one shared entangled pair plus classical communication to transmit an unknown qubit state exactly; and quantum repeaters, which extend entanglement (and hence teleportation) across distances too lossy for direct transmission.
Corresponds to Lectures 22–23. LOCC formalizes the physically realistic setting for distributed quantum protocols: separated parties can do anything they like to their own share of a system and talk to each other over an ordinary classical channel, but cannot send quantum states or act jointly — which is exactly weak enough that entanglement becomes a genuine, non-free resource under LOCC (quantifying this resource is entanglement-measures-and-distillation‘s job). Quantum teleportation is the headline LOCC protocol: given one shared entangled pair and two classical bits of communication, an arbitrary unknown qubit state can be transmitted exactly, without ever being measured or physically sent — consuming the entanglement in the process. Quantum repeaters solve the practical problem that directly distributing entanglement over long distances suffers exponential photon loss, by distributing entanglement over short hops and using entanglement swapping (teleportation applied to half of two separate pairs) to stitch them into one long-distance pair.
Outline (TODO — flesh out each)
- Local operations and classical communication (LOCC)
- Quantum teleportation
- Quantum repeaters and entanglement swapping