Further Results on the Cross Norm Criterion for Separability

By Oliver Rudolph. Quantum Information Processing, 2002

303 citations recorded by the source corpus.

In the present paper we develop and investigate a novel approach that aims to characterize quantum entanglement by using cross norms. In the first part of the paper we further develop the mathematical theory by determining the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that our techniques induce a novel powerful analytical and computable separability criterion for bipartite systems. This new criterion complements the well-known Peres positive partial transpose criterion in several aspects. It is a necessary but in general not a sufficient criterion for separability. We demonstrate the power of the new criterion by evaluating the criterion for a number of important examples. We also demonstrate that the new criterion is able to detect bound entangled states.

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

View Paper: https://www.semanticscholar.org/paper/2021392c8dda965cf147519629f199337dedeb90

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Citations in the corpus

Entanglement detection (2008, background): “Here, we want to explain the computable cross norm or realignment criterion (CCNR criterion) [54,55], since it is simple and strong.”
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].”
Quantum steering (2019, background): “This elegant inequality resembles the familiar computable cross norm or realignment (CCNR) entanglement criterion (Chen and Wu, 2003; Rudolph, 2005), where ∑ k λk > 1 implies that the state is entangled.”
A matrix realignment method for recognizing entanglement (2002, methodology): “The cross norm criterion proposed in [23] leads to the same result as our above Theorem, but with the expressions in Dirac bra-ket notation.”