Peres–Horodecki criterion

The Peres–Horodecki criterion is a necessary condition, for the joint <a href="/facts/Density_matrix/A1XdylJa">density matrix</a> 
 
 
 
 ρ
 
 
 {\displaystyle \rho }
 
 of two quantum mechanical systems 
 
 
 
 A
 
 
 {\displaystyle A}
 
 and 
 
 
 
 B
 
 
 {\displaystyle B}
 
, to be <a href="/facts/Separable_states/j0k8VWmF">separable</a>. It is also called the PPT criterion, for positive partial transpose. In the 2×2 and 2×3 dimensional cases the condition is also sufficient. It is used to decide the separability of <a href="/facts/Mixed_state_(physics)/7jbxd7Dx">mixed states</a>, where the <a href="/facts/Schmidt_decomposition/t7CYaV0F">Schmidt decomposition</a> does not apply. The theorem was discovered in 1996 by <a href="/facts/Asher_Peres/vPmVaDaM">Asher Peres</a> and the Horodecki family (<a href="/facts/Micha%25C5%2582_Horodecki/kekMHskT">Michał</a>, <a href="/facts/Pawe%25C5%2582_Horodecki/7HcBdKuM">Paweł</a>, and <a href="/facts/Ryszard_Horodecki/5GysBNxw">Ryszard</a>)
In higher dimensions, the test is inconclusive, and one should supplement it with more advanced tests, such as those based on <a href="/facts/Entanglement_witness/8Afsua0X">entanglement witnesses</a>.

Peres–Horodecki criterion open-in-new

Peres–Horodecki criterion