Bound Entanglement
Some entangled states cannot yield any pure Bell pairs no matter how many copies you process; their entanglement is locked away.
Entanglement you cannot cash out
Distillation is the process of converting many copies of a noisy entangled state into fewer high-quality Bell pairs using only local operations and classical communication. A striking discovery is that some entangled states are undistillable: no protocol extracts even one Bell pair, in any asymptotic limit. Their entanglement is real but bound, unable to be freed for tasks like teleportation.
The PPT connection
Every state with positive partial transpose is undistillable, because distillation cannot create a negative partial transpose from a positive one. In 2x2 and 2x3 systems all PPT states are separable, so bound entanglement cannot exist there. From 3x3 and 2x4 upward, entangled PPT states appear, and these are the canonical examples of bound entanglement, first constructed by the Horodecki family.
- Free entanglement: distillable, has negative partial transpose
- Bound entanglement: entangled but PPT, not distillable
- Separable: no entanglement, always PPT
Why it is not useless
Bound entangled states still require entangling operations to create, and they exhibit nonclassical features. They can activate the usefulness of other states, help in certain key-distribution settings, and probe the geometry of the state space. Their existence shows that entanglement is not a single scalar resource but has a rich structure with irreversibilities: you may need free entanglement to create a bound state that you can never fully recover.
Open questions
Whether all undistillable entangled states are PPT, or whether NPT (negative partial transpose) bound entanglement also exists, remains a long-standing open problem in quantum information. Its resolution would clarify how reversible the theory of entanglement is. For applied work the practical lesson is concrete: a nonzero negativity guarantees a distillable, useful resource, whereas zero negativity on a large system does not by itself certify the absence of entanglement.