arXiv:quant-ph/0411142

Generalised Smolin states and their properties

Remigiusz Augusiak, Paweł Horodecki

Published Nov 18, 2004• 1 citation

Abstract

Four qubit bound entangled Smolin states are generalised in a natural way to even number of qubits. They are shown to maximally violate simple correlation Bell inequalities and, as such, to reduce communication complexity, though they do not admit quantum security. They are also shown to serve for remote quantum information concentration like in the case of the original four qubit states. Application of the information concentration to the process of unlocking of classical correlations and quantum entanglement by quantum bit is pointed out.

DOI: 10.48550/arxiv.quant-ph/0411142

Related papers

Generalized Smolin states and their properties

Remigiusz Augusiak, Paweł Horodecki

Four-qubit bound entangled Smolin states are generalized with help of the Hilbert-Schmidt formalism to any even number of qubits. They are shown to maximally violate simple correlation Bell inequalities and, as such, to reduce communication complexity, although they do not admit quantum security. They are also shown to serve for remote quantum information concentration, as in the case of the original four-qubit states. It is proven that the latter effect allows us to unlock some entanglement measures and classical correlations. Also the possibility of quantum secret sharing by the considered state is pointed out.

Physical Review AJan 12, 200650 citations

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/0405187Physical Review AJul 28, 200679 citations

Generation and characterization of bound entanglement in optical qubits

Fumihiro Kaneda, Ryōsuke Shimizu, Yasuyoshi Mitsumori +2 more

For efficient quantum information processing (QIP), pure and strong entanglement in qubits has been thought to be indispensable.However, it was recently pointed out that bound entangled states, which involve undistillable entanglement between qubits, also have great potential for QIP.In this paper, we report the efficient generation of a four-qubit bound entangled state referred to as the Smolin state using photon polarization qubits.We observed the unlockable bound entanglement which is the specific property of the Smolin state.

Progress in InformaticsMar 1, 20113 citations

Proof of the insecurity of quantum secret sharing based on the Smolin bound entangled states

Yu Ya-Fei, Zhi‐Ming Zhang

This paper reconsiders carefully the possibility of using the Smolin bound entangled states as the carrier for sharing quantum secret. It finds that the process of quantum secret sharing based on Smolin states has insecurity though the Smolin state was reported to violate maximally the two-setting Bell-inequality. The general proof is given.

Chinese Physics BMar 17, 20093 citations

Bound entangled ststes of four qubits in tomographic probability representation

Igor V. Traskunov, Vladimir I. Man’ko

The entanglement phenomenon on example of Smolin state of four qubits is discussed. This state is known as bound entangled state and the spin tomogram of the state is found in explicit form. The qubit portrait method is used the Bell inequality violation which provides another tool to prove the property of entanglement of the four-qubit state under consideration.

arXiv:1204.1863Apr 9, 20120 citations

Bound entanglement can maximally violate Bell inequalities

Remigiusz Augusiak, Paweł Horodecki

It is shown that some four-qubit bound entangled states can maximally violate two-setting Bell inequality similar to standard CHSH inequality. Surprisingly this entanglement does not allow for secure key distillation, so neither entanglement nor violation of Bell inequalities implies quantum security. It is also pointed out how that kind of bound entanglement can be useful in reducing communication complexity.

May 30, 20040 citations