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Hyperentanglement for quantum information

Julio Tomas Barreiro-Guerrero

Published Jan 1, 2008• 3 citations
OpenAlex

Abstract

"Finally, we explore experimental schemes to create two novel states, ""bound-entangled"" and CGLMP states. The former are mixed states from which pure entanglement cannot be distilled; in particular, we consider the Smolin state, which is a mixture of hyperentangled states. The latter states present the puzzling property of violating a Bell-type inequality more strongly than would any maximally hyperentangled state."

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Nonlocality activation using local filtering operations based on CGLMP inequality

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Abstract Entanglement is necessary but not sufficient to demonstrate nonlocality as there exist local entangled states which do not violate any Bell inequality. In recent years, the activation of nonlocality (known as hidden nonlocality) by using local filtering operations has gained considerable interest. In the original proposal of Popescu [Phys. Rev. Lett. 74, 2619 (1995)] the hidden nonlocality was demonstrated for the Werner class of states in d ≥ 5. In this paper, we demonstrate the hidden nonlocality for a class of mixed entangled states (convex mixture of a pure state and color noise) in an arbitrary d-dimensional system using suitable local filtering operations. For our demonstration, we consider the quantum violation of Collins-Linden-Gisin-Masser-Popescu (CGLMP) inequality which has hitherto not been considered for this purpose. We show that when the pure state in the aforementioned mixed entangled state is a maximally entangled state, the range of the mixing parameter for revealing hidden nonlocality increases with increasing the dimension of the system. Importantly, we find that for d ≥ 8, hidden non-locality can be revealed for the whole range of mixing parameter. Further, by considering another pure state, the maximally CGLMP-violating state, we demonstrate the activation of nonlocality by using the same local filtering operation. We have also shown the activation of quantum fidelity for mixed entangled states using the same local filtering operator.

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Bound entanglement maximally violating Bell inequalities: Quantum entanglement is not fully equivalent to cryptographic security

Remigiusz Augusiak, Paweł Horodecki

It is shown that Smolin four-qubit bound entangled states [J. A. Smolin, Phys. Rev. A 63, 032306 (2001)] can maximally violate the simple two-setting Bell inequality similar to the standard Clauser-Horne-Shimony-Holt (CHSH) inequality. The simplicity of the setting and the robustness of the entanglement make it promising for current experimental technology. On the other hand, the entanglement does not allow for secure key distillation, so neither entanglement nor maximal violation of Bell inequalities implies directly the presence of a quantum secure key. As a result, one concludes that two tasks---reducing of communication complexity and cryptography---are not (even qualitatively) equivalent in a quantum multipartite scenario.

arXiv:quant-ph/0405187•Physical Review A•Jul 28, 2006•79 citations
"Finally, we explore experimental schemes to create two novel states, ""bound-entangled"" and CGLMP states. The former are mixed states from which pure entanglement cannot be distilled; in particular, we consider the Smolin state, which is a mixture of hyperentangled states. The latter states present the puzzling property of violating a Bell-type inequality more strongly than would any maximally hyperentangled state."
Quantum entanglement exhibits various interesting features that emerge only in high-dimensional systems. One of the most fascinating is bound entanglement, entanglement that cannot be extracted using local operations and classical communication. This thesis describes our work towards an experimental realization of the four-qubit bound-entangled Smolin state, using the polarization and spatial mode of photon pairs. We describe a number of interesting experimental challenges that this work faced. We present our results on entangled two-qubit spatial mode states and hyperentangled four-qubit polarization-spatial-mode states generated by spontaneous parametric down-conversion from a second-order TEM mode pump. Some of the subtleties involved in preparing genuine mixed states in the lab are discussed.
Entanglement is necessary but not sufficient to demonstrate nonlocality as there exist local entangled states which do not violate any Bell inequality. In recent years, the activation of nonlocality (known as hidden nonlocality) by using local filtering operations has gained considerable interest. In the original proposal of Popescu [Phys. Rev. Lett. 74, 2619 (1995)] the hidden nonlocality was demonstrated for the Werner class of states in d≥5d \geq 5d≥5. In this paper, we demonstrate the hidden nonlocality for a class of mixed entangled states (convex mixture of a pure state and color noise) in an arbitrary ddd-dimensional system using suitable local filtering operations. For our demonstration, we consider the quantum violation of Collins-Linden-Gisin-Masser-Popescu (CGLMP) inequality which has hitherto not been considered for this purpose. We show that when the pure state in the aforementioned mixed entangled state is a maximally entangled state, the range of the mixing parameter for revealing hidden nonlocality increases with increasing the dimension of the system. Importantly, we find that for d≥8d \geq 8d≥8, hidden non-locality can be revealed for the whole range of mixing parameter. Further, by considering another pure state, the maximally CGLMP-violating state, we demonstrate the activation of nonlocality by using the same local filtering operation.
Abstract Entanglement is necessary but not sufficient to demonstrate nonlocality as there exist local entangled states which do not violate any Bell inequality. In recent years, the activation of nonlocality (known as hidden nonlocality) by using local filtering operations has gained considerable interest. In the original proposal of Popescu [Phys. Rev. Lett. 74, 2619 (1995)] the hidden nonlocality was demonstrated for the Werner class of states in d ≥ 5. In this paper, we demonstrate the hidden nonlocality for a class of mixed entangled states (convex mixture of a pure state and color noise) in an arbitrary d-dimensional system using suitable local filtering operations. For our demonstration, we consider the quantum violation of Collins-Linden-Gisin-Masser-Popescu (CGLMP) inequality which has hitherto not been considered for this purpose. We show that when the pure state in the aforementioned mixed entangled state is a maximally entangled state, the range of the mixing parameter for revealing hidden nonlocality increases with increasing the dimension of the system. Importantly, we find that for d ≥ 8, hidden non-locality can be revealed for the whole range of mixing parameter. Further, by considering another pure state, the maximally CGLMP-violating state, we demonstrate the activation of nonlocality by using the same local filtering operation. We have also shown the activation of quantum fidelity for mixed entangled states using the same local filtering operator.
It is shown that Smolin four-qubit bound entangled states [J. A. Smolin, Phys. Rev. A 63, 032306 (2001)] can maximally violate the simple two-setting Bell inequality similar to the standard Clauser-Horne-Shimony-Holt (CHSH) inequality. The simplicity of the setting and the robustness of the entanglement make it promising for current experimental technology. On the other hand, the entanglement does not allow for secure key distillation, so neither entanglement nor maximal violation of Bell inequalities implies directly the presence of a quantum secure key. As a result, one concludes that two tasks---reducing of communication complexity and cryptography---are not (even qualitatively) equivalent in a quantum multipartite scenario.