I saw this today, thought some of you might find it interesting (as I did).(adsbygoogle = window.adsbygoogle || []).push({});

Product states do not violate Bell inequalities. Entangled states do, and this draws a clear line between the quantum world and the classical world.

So imagine my surprise with this: a paper that shows that even Product States can cross the line between the quantum world and the classical world.

Quantumness of Product States

Jing-Ling Chen, Hong-Yi Su, Chunfeng Wu, C. H. Oh

http://arxiv.org/abs/1204.1798

From the paper:

Abstract: Product states do not violate Bell inequalities. In this work, we investigate the quantumness of product states by violating a certain classical algebraic models. Thus even for product states, statistical predictions of quantum mechanics and classical theories do not agree. An experiment protocol is proposed to reveal the quantumness...[itex]\:[/itex]

...a classical model must satisfy the AR [Alicki-Van Ryn] inequality

[itex](1) <A>\: ≥\: 0,[/itex]

[itex](2) <B>\: ≥\: 0,[/itex]

[itex](3) <B − A>\: ≥\: 0, [/itex]

[itex](4) <B^2 − A^2>\: ≥\: 0[/itex]

However, in quantum mechanics there exist noncommutative observables that violate the fourth constraint, namely, one can find positive-definite observables A and B satisfying [the first three but not the last]. This violation is called quantumness. Experimental tests have been performed for the case of one qubit...

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# Quantumness of Product States

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