Distillable entanglement of quantum state

Alice and Bob start from n copies of a Quantum_state: ρ^⊗n.

They apply a LOCC Λ to distill entanglement.

How many bottles of distilled entanglement can they fill up?

import LOCC

def distillable_entanglement [quantum_state ρ] : ℝ :=
sup {r | lim n→∞ inf {∥Λ(ρ^⊗n) - Φ^⊗(r*n)∥₁ | LOCC Λ} = 0}

• We can have distillable_entanglement ρ = 0

• Dual measure to Entanglement cost of quantum state;

• Upper bounded by Rains relative entropy;

References

• Lami2021;

• Horodecki2007;