Greenberger-Horne-Zeilinger theorem for N-partite quDits

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 one 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 $N$ .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 one 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 $N$.

arXiv:1303.5326Physical Review AOct 2, 201324 citations

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 one 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