Abstract:

We use duality techniques to prove and generalize the cross norm and computable cross norm criteria for separability of quantum states. While the original proof of the cross norm criterion is long and involved, our new proof is short and elementary. Furthermore, our proof generalizes naturally to arbitrary Schmidt number. We also use these techniques to generalize the computable cross norm criterion to arbitrary Schmidt number and prove some results of independent interest along the way.

Authors:

• Nathaniel Johnston

Download:

• Official publication at Linear and Multilinear Algebra
• Local preprint [pdf]
• Slideshow presentation [pdf]

Cite as:

• N. Johnston. Norm duality and the cross norm criteria for quantum entanglement. Linear and Multilinear Algebra (Proceedings of the 12th Workshop on Numerical Ranges and Numerical Radii), 2013. doi: 10.1080/03081087.2012.753595

Related publications:

• Duality of Entanglement Norms – a full journal article with many related results