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- W2949203789 abstract "We present a survey on mathematical topics relating to separable states and entanglement witnesses. The convex cone duality between sepa- rable states and entanglement witnesses is discussed and later generalized to other families of operators, leading to their characterization via multiplicative properties. The condition for an operator to be an entanglement witness is rephrased as a problem of positivity of a family of real polynomials. By solv- ing the latter in a specic case of a three-parameter family of operators, we obtain explicit description of entanglement witnesses belonging to that family. A related problem of block positivity over real numbers is discussed. We also consider a broad family of block positivity tests and prove that they can never be sucient, which should be useful in case of future eorts i n that direction. Finally, we introduce the concept of length of a separable state and present new results concerning relationships between the length and Schmidt rank. In particular, we prove that separable states of length lower of equal 3 have Schmidt ranks equal to their lengths. We also give an example of a state which has length 4 and Schmidt rank 3." @default.
- W2949203789 created "2019-06-27" @default.
- W2949203789 creator A5091229656 @default.
- W2949203789 date "2010-01-20" @default.
- W2949203789 modified "2023-09-27" @default.
- W2949203789 title "DUALITIES AND POSITIVITY IN THE STUDY OF QUANTUM ENTANGLEMENT" @default.
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