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arXiv · 1303.5326

Greenberger-Horne-Zeilinger theorem for N qudits

Junghee Ryu·Changhyoup Lee·Marek Zukowski·Jinhyoung Lee
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Abstract

We generalize Greenberger-Horne-Zeilinger (GHZ) theorem to an arbitrary number of D-dimensional systems. Contrary to conventional approaches using compatible composite observables, we employ incompatible and concurrent observables, whose common eigenstate is still a generalized GHZ state. It is these concurrent observables which enable to prove a genuinely N-partite and D-dimensional GHZ theorem. Our principal idea is illustrated for a four-partite system with D which is an arbitrary multiple of 3. By extending to N qudits, we show that GHZ theorem holds as long as N is not divisible by all nonunit divisors of D, smaller than N.

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Junghee Ryu, Changhyoup Lee, Marek Zukowski, Jinhyoung Lee. 2013-10-07. Greenberger-Horne-Zeilinger theorem for N qudits. https://doi.org/10.1103/physreva.88.042101

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