**Separability Criterion**

The problem of deciding whether a state is separable in general is sometimes called **the separability problem** in quantum information theory. It is considered to be a difficult problem. It has been shown to be NP-hard. Some appreciation for this difficulty can be obtained if one attempts to solve the problem by employing the direct brute force approach, for a fixed dimension. We see that the problem quickly becomes intractable, even for low dimensions. Thus more sophisticated formulations are required. The separability problem is a subject of current research.

A *separability criterion* is a necessary condition a state must satisfy to be separable. In the low dimensional (*2 X 2* and *2 X 3*) cases, the Peres-Horodecki criterion is actually a necessary and sufficient condition for separability. Other separability criteria include the range criterion and reduction criterion.

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### Famous quotes containing the word criterion:

“Faith in reason as a prime motor is no longer the *criterion* of the sound mind, any more than faith in the Bible is the *criterion* of righteous intention.”

—George Bernard Shaw (1856–1950)