 Entanglement monotone

An entanglement monotone quantifies entanglement without increasing on average under local operations and classical communication. The average is over recorded measurement in quantum mechanics outcomes: individual successful branches can have more entanglement, provided their probabilities compensate for that increase. This distinction makes an entanglement monotone useful for bounding probabilistic state conversion. A pure-state entanglement monotone need only satisfy this inequality on pure input states and pure conditional branches, with local measurement outcomes refined to individual Kraus operators.

Entanglement monotones are a class of measures used in quantum information theory to quantify the amount of entanglement present in a quantum state. The key properties that define an entanglement monotone include: 1. **Non-negativity**: An entanglement monotone must be non-negative for all quantum states. In essence, it should assign a value of zero to separable states (states that are not entangled) and a positive value to entangled states.