scholarly journals Greenberger–Horne–Zeilinger states: Their identifications and robust violations

2021 ◽  
Author(s):  
Xing-Yan Fan ◽  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Chunfeng Wu ◽  
Arun Kumar Pati ◽  
...  
Keyword(s):  
Quantum Key Distribution ◽  
Quantum Information Processing ◽  
Quantum Secret Sharing ◽  
Entangled States ◽  
Ghz States ◽  
Quantum Phenomenon ◽  
Qubit System ◽  
Chsh Inequality ◽  
Maximal Violation ◽  
Maximally Entangled States

The [Formula: see text]-qubit Greenberger–Horne–Zeilinger (GHZ) states are the maximally entangled states of [Formula: see text] qubits, which have had many important applications in quantum information processing, such as quantum key distribution and quantum secret sharing. Thus how to distinguish the GHZ states from other quantum states becomes a significant problem. In this work, by presenting a family of the generalized Clauser–Horne–Shimony–Holt (CHSH) inequality, we show that the [Formula: see text]-qubit GHZ states can be indeed identified by the maximal violations of the generalized CHSH inequality under some specific measurement settings. The generalized CHSH inequality is simple and contains only four correlation functions for any [Formula: see text]-qubit system, thus has the merit of facilitating experimental verification. Furthermore, we present a quantum phenomenon of robust violations of the generalized CHSH inequality in which the maximal violation of Bell’s inequality can be robust under some specific noises adding to the [Formula: see text]-qubit GHZ states.

scholarly journals MAXIMALLY ENTANGLED STATES AND BELL'S INEQUALITY IN RELATIVISTIC REGIME

2009 ◽  
Vol 07 (01) ◽  
pp. 395-401 ◽  
Author(s):  
SHAHPOOR MORADI
Keyword(s):  
Ghz State ◽  
Entangled States ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Expectation Value ◽  
Spin Observables ◽  
Chsh Inequality ◽  
Relativistic Regime ◽  
Maximal Violation ◽  
Maximally Entangled States

In this letter we show that in the relativistic regime, maximally entangled state of two spin-1/2 particles not only gives maximal violation of the Bell-CHSH inequality but also gives the largest violation attainable for any pairs of four spin observables that are noncommuting for both systems. Also, we extend our results to three spin-1/2 particles. We obtain the largest eigenvalue of Bell operator and show that this value is equal to the expectation value of Bell operator on GHZ state.

scholarly journals Graph Approach to Quantum Teleportation Dynamics

2020 ◽  
Vol 2 (3) ◽  
pp. 352-377
Author(s):  
Efrén Honrubia ◽  
Ángel S. Sanz
Keyword(s):  
Quantum Information ◽  
Quantum Teleportation ◽  
Entangled States ◽  
Quantum Channels ◽  
Qubit System ◽  
Alternative Approaches ◽  
Maximally Entangled States ◽  
Usual State ◽  
Vector Description ◽  
Direct Correspondence

Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations that are aimed at allowing us a better understanding of the physics involved in the process from different perspectives. With this purpose, here an approach based on graph theory is introduced and discussed in the context of some applications. Its main goal is to provide a fully symbolic framework for quantum teleportation from a dynamical viewpoint, which makes explicit at each stage of the process how entanglement and information swap among the qubits involved in it. In order to construct this dynamical perspective, it has been necessary to define some auxiliary elements, namely virtual nodes and edges, as well as an additional notation for nodes describing potential states (against nodes accounting for actual states). With these elements, not only the flow of the process can be followed step by step, but they also allow us to establish a direct correspondence between this graph-based approach and the usual state vector description. To show the suitability and versatility of this graph-based approach, several particular teleportation examples are examined in detail, which include bipartite, tripartite, and tetrapartite maximally entangled states as quantum channels. From the analysis of these cases, a general protocol is devised to describe the sharing of quantum information in presence of maximally entangled multi-qubit system.

Bipartite entanglement of decohered mixed states generated from maximally entangled cluster states

2021 ◽  
Vol 36 (03) ◽  
pp. 2150010
Author(s):  
Mostafa Mansour ◽  
Saeed Haddadi
Keyword(s):  
Mixed State ◽  
Entangled States ◽  
Entangled State ◽  
Mixed States ◽  
Density Matrices ◽  
Bipartite Entanglement ◽  
Cluster States ◽  
Maximally Entangled State ◽  
Qubit System ◽  
Maximally Entangled States

In this work, we investigate the bipartite entanglement of decohered mixed states generated from maximally entangled cluster states of [Formula: see text] qubits physical system. We introduce the disconnected cluster states for an ensemble of [Formula: see text] non-interacting qubits and we give the corresponding separable density matrices. The maximally entangled states can be generated from disconnected cluster states, by assuming that the dynamics of the multi-qubit system is governed by a quadratic Hamiltonian of Ising type. When exposed to a local noisy interaction with the environment, the multi-qubit system evolves from its initial pure maximally entangled state to a decohered mixed state. The decohered mixed states generated from bipartite, tripartite and multipartite maximally entangled cluster states are explicitly expressed and their bipartite entanglements are investigated.

New approach to quantum key distribution via quantum encryption

2009 ◽  
Vol 9 (9&10) ◽  
pp. 879-898
Author(s):  
A. Fahmi
Keyword(s):  
Secret Sharing ◽  
Quantum Key Distribution ◽  
Bell State ◽  
Quantum Secret Sharing ◽  
Key Distribution ◽  
Channel Noise ◽  
New Approach ◽  
Ghz States ◽  
Higher Dimensional ◽  
Special Strategy

Recently, Zhang, Li and Guo (ZLG) suggested a new approach to quantum key distribution by using a shared Bell state which acts as quantum key in order to encode and decode classical information. Subsequently, others extended ZLG protocol to d-dimensional systems and to quantum secret sharing based on reusable GHZ states. However, Gao et al. have shown that if Eve employs a special strategy to attack, these protocols become insecure. Afterwards, they repair ZLG protocol so that their eavesdropping strategy becomes inefficient. In this paper, we investigate the security of ZLG quantum key distribution protocol and show that it is not secure against Eve's attacks and with probability of one half she gets all of the keys without being detected by the two parties. In this eavesdropping strategy, Eve transforms the previously shared Bell state between Alice and Bob to two Bell states among herself and the parties. Moreover, we briefly show that ZLG's repairing by Gao et al's is not efficient against of our attack and Eve can choose an appropriate rotation angle and measurement bases which help her to do eavesdropping. Afterwards, we discuss generalization of ZLG protocol to d-dimensional systems and show that with probability 1/d, Eve gets all of keys. We show that quantum secret sharing based on reusable GHZ states is also not secure and with probability one half, Eve gets all of keys. We repair them by going to higher dimensional shared EPR or GHZ states. Finally, we compare ZLG protocol with ours and show that the ZLG protocol and its extensions are less robust against the channel noise with respect to ours.

Correlations, Nonlocality and Usefulness of an Efficient Class of Two-Qubit Mixed Entangled States

2018 ◽  
Vol 73 (3) ◽  
pp. 191-206 ◽  
Author(s):  
Parvinder Singh ◽  
Atul Kumar
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Weak Measurement ◽  
Analytical Relation ◽  
Entangled States ◽  
Mixed States ◽  
New Class ◽  
Chsh Inequality ◽  
Noisy Conditions

AbstractWe establish an analytical relation between the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality and weak measurement strengths under noisy conditions. We show that the analytical results obtained in this article are of utmost importance for proposing a new class of two-qubit mixed states for quantum information processing. Our analysis further shows that the states proposed here are better resources for quantum information in comparison to other two-qubit mixed entangled states.

Experimental test of CHSH inequality for non-maximally entangled states

2001 ◽  
Vol 287 (5-6) ◽  
pp. 317-320 ◽  
Author(s):  
Yun-Feng Huang ◽  
Chuan-Feng Li ◽  
Yong-Sheng Zhang ◽  
Guang-Can Guo
Keyword(s):  
Experimental Test ◽  
Entangled States ◽  
Chsh Inequality ◽  
Maximally Entangled States

scholarly journals Local Information as an Essential Factor for Quantum Entanglement

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 728
Author(s):  
Zhaofeng Su
Keyword(s):  
Quantum Entanglement ◽  
Quantum Information Processing ◽  
Local Information ◽  
Essential Factor ◽  
Qubit System ◽  
Local Vectors ◽  
Correlation Parameters ◽  
The One ◽  
Local Parameters

Quantum entanglement is not only a fundamental concept in quantum mechanics but also a special resource for many important quantum information processing tasks. An intuitive way to understand quantum entanglement is to analyze its geometric parameters which include local parameters and correlation parameters. The correlation parameters have been extensively studied while the role of local parameters have not been drawn attention. In this paper, we investigate the question how local parameters of a two-qubit system affect quantum entanglement in both quantitative and qualitative perspective. Firstly, we find that the concurrence, a measure of quantum entanglement, of a general two-qubit state is bounded by the norms of local vectors and correlations matrix. Then, we derive a sufficient condition for a two-qubit being separable in perspective of local parameters. Finally, we find that different local parameters could make a state with fixed correlation matrix separable, entangled or even more qualitatively entangled than the one with vanished local parameters.

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