Greenberger-Horne-Zeilinger-type Violation of Local Realism for Two Photons

It is shown that the Greenberger-Horne-Zeilinger theorem can be generalized to the case with only two entangled particles. The reasoning makes use of two photons which are maximally entangled both in polarization and in spatial degrees of freedom. In contrast to Cabello's argument of "all versus nothing" nonlocality with four photons [Phys. Rev. Lett. 87, 010403 (2001)]], our proposal to test the theorem can be implemented with linear optics and thus is well within the reach of current experimental technology.It is shown that the Greenberger-Horne-Zeilinger theorem can be generalized to the case with only two entangled particles. The reasoning makes use of two photons which are maximally entangled both in polarization and in spatial degrees of freedom. In contrast to Cabello's argument of "all versus nothing" nonlocality with four photons [Phys. Rev. Lett. 87, 010403 (2001)]], our proposal to test the theorem can be implemented with linear optics and thus is well within the reach of current experimental technology.

arXiv:quant-ph/0211075Physical Review LettersApr 24, 200377 citations

General proof of the Greenberger-Horne-Zeilinger theorem

Zeqian Chen

It is proved that all states of three spin- $\frac{1}{2}$ particles exhibiting an ``all versus nothing'' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality.It is proved that all states of three spin-$\frac{1}{2}$ particles exhibiting an ``all versus nothing'' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality.

Physical Review ASep 24, 20041 citation

Experiments of quantum nonlocality with polarization-momentum entangled photon pairs

Giuseppe Vallone, Paolo Mataloni, F. De Martini +1 more

We present the results of some experimental tests of quantum nonlocality performed by two-photon states, entangled both in polarization and momentum, namely hyperentangled states and two-photon four-qubit linear cluster states. These states, which double the number of available qubits with respect to the standard two-photon entangled states, are engineered by a simple experimental method, which adopts linear optics and a single type I nonlinear crystal. The tests of local realism performed with these states represent a generalization of the Greenberger, Home, and Zeilinger (GHZ) theorem to the case of two entangled particles.We present the results of some experimental tests of quantum nonlocality performed by two-photon states, entangled both in polarization and momentum, namely hyperentangled states and two-photon four-qubit linear cluster states. These states, which double the number of available qubits with respect to the standard two-photon entangled states, are engineered by a simple experimental method, which adopts linear optics and a single type I nonlinear crystal. The tests of local realism performed with these states represent a generalization of the Greenberger, Home, and Zeilinger (GHZ) theorem to the case of two entangled particles.

Laser PhysicsJul 1, 20070 citations

Experimental Violation of Local Realism by Four-Photon Greenberger-Horne-Zeilinger Entanglement

Zhi Zhao, Tao Yang, Yu-Ao Chen +3 more

We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.

arXiv:quant-ph/0302137Physical Review LettersOct 28, 2003215 citations

Greenberger-Horne-Zeilinger theorem cannot be extended to a Bell state

Zeqian Chen

The Greenberger-Horne-Zeilinger (GHZ) theorem exhibits an ``all versus nothing'' contradiction between Ernstein, Podelsky, and Rosen's local realism and quantum mechanics by using a maximally entangled state of three qubits. However, it is shown in this paper that no extension of GHZ's proof is possible for any entangled state of two qubits, including Bell states. The proof is obtained by showing the fact that there are no more than three distinct elements (except for a different sign) in a set of mutually commuting nonlocal spin observables of two qubits. This also leads to a generic setup of the Kochen-Specker theorem for the two-qubit system.The Greenberger-Horne-Zeilinger (GHZ) theorem exhibits an ``all versus nothing'' contradiction between Ernstein, Podelsky, and Rosen's local realism and quantum mechanics by using a maximally entangled state of three qubits. However, it is shown in this paper that no extension of GHZ's proof is possible for any entangled state of two qubits, including Bell states. The proof is obtained by showing the fact that there are no more than three distinct elements (except for a different sign) in a set of mutually commuting nonlocal spin observables of two qubits. This also leads to a generic setup of the Kochen-Specker theorem for the two-qubit system.

Physical Review ANov 17, 20035 citations

Observation of Three-Photon Greenberger-Horne-Zeilinger Entanglement

Dik Bouwmeester, Jian-Wei Pan, Matthew Daniell +2 more

We present the experimental observation of polarization entanglement for three spatially separated photons. Such states of more than two entangled particles, known as Greenberger-Horne-Zeilinger (GHZ) states, play a crucial role in fundamental tests of quantum mechanics versus local realism and in many quantum information and quantum computation schemes. Our experimental arrangement is such that we start with two pairs of entangled photons and register the photons in a way that any information as to which pair each photon belongs to is erased. After detecting a trigger photon, the registered events at the detectors for the remaining three photons exhibit the desired GHZ correlations.We present the experimental observation of polarization entanglement for three spatially separated photons. Such states of more than two entangled particles, known as Greenberger-Horne-Zeilinger (GHZ) states, play a crucial role in fundamental tests of quantum mechanics versus local realism and in many quantum information and quantum computation schemes. Our experimental arrangement is such that we start with two pairs of entangled photons and register the photons in a way that any information as to which pair each photon belongs to is erased. After detecting a trigger photon, the registered events at the detectors for the remaining three photons exhibit the desired GHZ correlations.

arXiv:quant-ph/9810035Physical Review LettersFeb 15, 19991,061 citations

It is proved that all states of three spin-

\frac{1}{2}

particles exhibiting an ``all versus nothing'' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality.