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I saw this today, thought some of you might find it interesting (as I did).
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...
...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...[itex]\:[/itex]
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...
...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...[itex]\:[/itex]
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