Entanglement monotone

In quantum information and quantum computation, an entanglement monotone is a function that quantifies the amount of entanglement present in a quantum state. Any entanglement monotone is a nonnegative function whose value does not increase under local operations and classical communication.
Definition.
Let formula_1be the space of all states, i.e., Hermitian positive semi-definite operators with trace one, over the bipartite Hilbert space formula_2. An entanglement measure is a function formula_3such that:
Some authors also add the condition that formula_15 over the maximally entangled state formula_16. If the nonnegative function only satisfies condition 2 of the above, then it is called an entanglement monotone.