Entanglement Measures and Distillation
Stub. Quantifying entanglement rather than just detecting it: entanglement measures and monotones, functions that are non-increasing under LOCC (so they correctly treat entanglement as a resource that LOCC alone can't create) — and entanglement distillation, LOCC protocols for converting many copies of a weakly/noisily entangled state into fewer copies of (closer to) maximally entangled pairs usable for teleportation.
Corresponds to Lectures 26–27, the course’s final unit. An entanglement monotone is any function of a (possibly mixed, multi- party) state that cannot increase under LOCC — the defining property any reasonable “amount of entanglement” measure must have, since LOCC is exactly the class of operations that shouldn’t be able to create entanglement from nothing. Covers the standard examples (entanglement of formation, distillable entanglement, and others) and how they relate. Entanglement distillation is the LOCC protocol answering the practical question this machinery sets up: given many copies of a partially entangled or noisy state (e.g. degraded by transmission through the lossy channels of quantum-channels-cp-maps-and-representations), extract a smaller number of copies that are (almost) maximally entangled, usable for teleportation or repeater protocols — the key subroutine that makes long-distance quantum networking feasible despite unavoidable noise.
Outline (TODO — flesh out each)
- Entanglement measures and monotones
- Entanglement of formation; distillable entanglement
- Entanglement distillation protocols