Entanglement Monotone

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Definition

For a general density matrix, ρ, which can be divided into two or more sub-systems, the quantity EX(ρ) (the label X is used to denote a generic measure) qualifies as an entanglement monotone if it satisfies the conditions

C1

E_{X}(\rho) \geq 0;
EX(ρ) = 0 if ρ is separable;
E_{X}(\mathrm{Bell\,State}) = 1.

C2

Local operations, classical communication and post-selection (LOCC) do not increase EX(ρ) on average. For example, with any state, ρ, and partition, {A,B}, local unitary transformations, \hat{U} = \hat{U}_A \otimes \hat{U}_B, do not affect EX(ρ).

C3

Entanglement is convex under discarding information, \sum_i p_i E_{X}(\rho_i) \geq E_{X}(\sum_i p_i \rho_i).

The Bell States are defined here.

List of Monotones

Here's a list of entanglement monotones which should eventually turn into a comparison chart of sorts.

Also see the entanglement monotone category.

References

1) G. Vidal, quant-ph/9807077, (1999).
2) M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 84, 2014 (2000).
3) T. Wei, K. Nemoto, P. Goldbart, P. Kwiat, W. Munro, and F. Verstraete, quant-ph/0208138, (2002).

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