Some properties of the computable cross-norm criterion for separability

By Oliver Rudolph. 2002

184 citations recorded by the source corpus.

The computable cross-norm (CCN) criterion is a powerful analytical and computable separability criterion for bipartite quantum states, which is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension $2\ifmmode\times\else\texttimes\fi{}2.$ In higher dimensions, theorems connecting the fidelity of a quantum state with the CCN criterion are proved. We also analyze the behavior of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3dceb6c665b2b1b277ccd91a75506ccf9fa69c48

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Geometry of Quantum States: Index (2007, background): “26 Called also realignment criterion [206] or computable cross-norm criterion [781].”
Entanglement detection (2008, background): “However, it does not detect all entangled states of two-qubits [64].”
Entanglement certification from theory to experiment (2018, methodology): “A prominent example of the above method is the so called computable cross-norm or realignment (CCNR) criterion [89–92].”