Recent years have witnessed a rapidly growing interest in high-dimensional quantum entanglement for fundamental studies as well as towards novel applications. Therefore, the ability to verify entanglement between physical qudits, $d$ -dimensional quantum systems, is of crucial importance. To show nonclassicality, Hardy's paradox represents ``the best version of Bell's theorem'' without using inequalities. However, so far it has only been tested experimentally for bidimensional vector spaces. Here, we formulate a theoretical framework to demonstrate the ladder proof of Hardy's paradox for arbitrary high-dimensional systems. Furthermore, we experimentally demonstrate the ladder proof by taking advantage of the orbital angular momentum of high-dimensionally entangled photon pairs. We perform the ladder proof of Hardy's paradox for dimensions 3 and 4, both with the ladder up to the third step. Our paper paves the way towards a deeper understanding of the nature of high-dimensionally entangled quantum states and may find applications in quantum information science.Recent years have witnessed a rapidly growing interest in high-dimensional quantum entanglement for fundamental studies as well as towards novel applications. Therefore, the ability to verify entanglement between physical qudits, $d$-dimensional quantum systems, is of crucial importance. To show nonclassicality, Hardy's paradox represents ``the best version of Bell's theorem'' without using inequalities. However, so far it has only been tested experimentally for bidimensional vector spaces. Here, we formulate a theoretical framework to demonstrate the ladder proof of Hardy's paradox for arbitrary high-dimensional systems. Furthermore, we experimentally demonstrate the ladder proof by taking advantage of the orbital angular momentum of high-dimensionally entangled photon pairs. We perform the ladder proof of Hardy's paradox for dimensions 3 and 4, both with the ladder up to the third step. Our paper paves the way towards a deeper understanding of the nature of high-dimensionally entangled quantum states and may find applications in quantum information science.

Physical Review AAug 9, 201716 citations

Quantum Analogues of Hardy’s Nonlocality Paradox

T. A. Fritz

arXiv:1006.2497Foundations of PhysicsMay 19, 20119 citations

Experimentally testing Hardy’s theorem on nonlocality with entangled mixed states

Dai-He Fan, Maochun Dai, Wei-Jie Guo +1 more

Hardy’s theorem on nonlocality has been verified by a series of experiments with two-qubit entangled pure states. However, in this paper we demonstrate the experimental test of the theorem by using the two-photon entangled mixed states. We first investigate the generic logic in Hardy’s proof of nonlocality, which can be applied for arbitrary two-qubit mixed polarization entangled states and can be reduced naturally to the well-known logic tested successfully by the previous pure state experiments. Then, the optimized violations of locality for various experimental parameters are delivered by the numerical method. Finally, the logic argued above for testing Hardy’s theorem on nonlocality is demonstrated experimentally by using the mixed entangled-photon pairs generated via pumping two type-I BBO crystals. Our experimental results shows that Hardy’s proof of nonlocality can also be verified with two-qubit polarization entangled mixed states, with a violation of about 3.4 standard deviations.Hardy’s theorem on nonlocality has been verified by a series of experiments with two-qubit entangled pure states. However, in this paper we demonstrate the experimental test of the theorem by using the two-photon entangled mixed states. We first investigate the generic logic in Hardy’s proof of nonlocality, which can be applied for arbitrary two-qubit mixed polarization entangled states and can be reduced naturally to the well-known logic tested successfully by the previous pure state experiments. Then, the optimized violations of locality for various experimental parameters are delivered by the numerical method. Finally, the logic argued above for testing Hardy’s theorem on nonlocality is demonstrated experimentally by using the mixed entangled-photon pairs generated via pumping two type-I BBO crystals. Our experimental results shows that Hardy’s proof of nonlocality can also be verified with two-qubit polarization entangled mixed states, with a violation of about 3.4 standard deviations.

Chinese Physics BApr 1, 20172 citations

Testing Quantum Nonlocality with Two Qubit X Sstates

刘晋 LIU Jin, 缪波 MIU Bo, 胡强 Hu Qiang +1 more

Acta Sinica Quantum OpticaJan 1, 20202 citations

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-dimensional quantum systems, is of crucial importance. To show nonclassicality, Hardy's paradox represents ``the best version of Bell's theorem'' without using inequalities. However, so far it has only been tested experimentally for bidimensional vector spaces. Here, we formulate a theoretical framework to demonstrate the ladder proof of Hardy's paradox for arbitrary high-dimensional systems. Furthermore, we experimentally demonstrate the ladder proof by taking advantage of the orbital angular momentum of high-dimensionally entangled photon pairs. We perform the ladder proof of Hardy's paradox for dimensions 3 and 4, both with the ladder up to the third step. Our paper paves the way towards a deeper understanding of the nature of high-dimensionally entangled quantum states and may find applications in quantum information science.