The computational power of the W and GHZ states

2006 ◽  
Vol 6 (2) ◽  
pp. 173-183
Author(s):  
E. D'Hondt ◽  
P. Panangaden
Keyword(s):  
Pure State ◽  
Lie Symmetry ◽  
Leader Election ◽  
Ghz State ◽  
W State ◽  
Computational Power ◽  
Post Processing ◽  
Distributed Consensus ◽  
Quantum Networks ◽  
Impossibility Results

It is well understood that the use of quantum entanglement significantly enhances the computational power of systems. Much of the attention has focused on Bell states and their multipartite generalizations. However, in the multipartite case it is known that there are several inequivalent classes of states, such as those represented by the W-state and the GHZ-state. Our main contribution is a demonstration of the special computational power of these states in the context of paradigmatic problems from classical distributed computing. Concretely, we show that the W-state is the only pure state that can be used to exactly solve the problem of leader election in anonymous quantum networks. Similarly we show that the GHZ-state is the only one that can be used to solve the problem of distributed consensus when no classical post-processing is considered. These results generalize to a family of W- and GHZ-like states. At the heart of the proofs of these impossibility results lie symmetry arguments.

MULTIPLE CONCURRENCE OF MULTI-PARTITE QUANTUM SYSTEM

2010 ◽  
Vol 08 (07) ◽  
pp. 1169-1177 ◽  
Author(s):  
HUA WU ◽  
XIN ZHAO ◽  
YAN-SONG LI ◽  
GUI-LU LONG
Keyword(s):  
Quantum System ◽  
Pure State ◽  
Arbitrary Number ◽  
Cluster State ◽  
Ghz State ◽  
W State ◽  
Entanglement Property ◽  
Analytical Results ◽  
Global Entanglement ◽  
Number Of Particles

We propose a new way of description of the global entanglement property of a multi-partite pure state quantum system. Based on the idea of bipartite concurrence, by dividing the multi-partite quantum system into two subsystems, a combination of all the bipartite concurrences of a multi-partite quantum system is used to describe the entanglement property of the multi-partite system. We derive the analytical results for GHZ-state, W-state with arbitrary number of qubits, and cluster state with the number of particles no greater than 6.

Evolution of Genuine Multipartite Entanglement of Specific and Random States Under non-Markovian Noise

2014 ◽  
Vol 21 (04) ◽  
pp. 1450008 ◽  
Author(s):  
Mazhar Ali
Keyword(s):  
Mixed State ◽  
Weighted Graph ◽  
Ghz State ◽  
W State ◽  
Multipartite Entanglement ◽  
Fragile State ◽  
Graph States ◽  
Random States ◽  
Genuine Multipartite Entanglement

We study the dynamics of genuine multipartite entanglement under non-Markovian noise. Using a computable entanglement monotone for multipartite systems, we investigate a system of three qubits each of which is individually exposed to classical Ornstein–Uhlenbeck noise. We found that the W state mixed with the maximally mixed state is the most fragile state, whereas a similar mixture of GHZ state exhibits robust behaviour. We compare dynamics of these states with dynamics of similar mixtures of random states and weighted graph states. We also discuss the limiting cases.

Dynamics of multi-qubit states in non-inertial frames for quantum communication applications

2014 ◽  
Vol 14 (3&4) ◽  
pp. 255-264
Author(s):  
Alaa Sagheer ◽  
Hala Hamdoun
Keyword(s):  
Degradation Rate ◽  
Quantum Communication ◽  
Ghz State ◽  
The Other ◽  
W State ◽  
Entangled States ◽  
Inertial Frames ◽  
Qubit States ◽  
Degree Of Entanglement ◽  
Accelerated Frames

In this paper, some properties of multi-qubit states traveling in non-inertial frames are investigated, where we assume that all particles are accelerated. These properties are including fidelities, capacities and entanglement of the accelerated channels for three different states, namely, Greeberger-Horne-Zeilinger (GHZ) state, GHZ-like state and W-state. It is shown here that all these properties are decreased as the accelerations of the moving particles are increased. The obtained results show that the GHZ-state is the most robust state comparing to the others, where the degradation rate is less than that for the other states particularly in the second Rindler region. Also, it is shown here that the entangled property doesn't change in the accelerated frames. Additionally, the paper shows that the degree of entanglement decreases as the accelerations of the particles increase in the first Rindler region. However in the second region, where all subsystems are disconnected at zero acceleration, entangled states are generated as the acceleration increases.

Entanglement witnesses of four-qubit tripartite separable quantum states

2021 ◽  
Author(s):  
Miao Xu ◽  
Wei-feng Zhou ◽  
Feng Chen ◽  
Lizhen Jiang ◽  
Xiao-yu Chen
Keyword(s):  
Necessary Conditions ◽  
Quantum Systems ◽  
Ghz State ◽  
W State ◽  
Necessary Condition ◽  
Entangled State ◽  
Separable State ◽  
Entanglement Witnesses ◽  
Qubit System ◽  
Bipartite Quantum Systems

Abstract A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Comparing to the entanglement of bipartite quantum systems, less progresses have been made for the entanglement of multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, it is proved that the necessary conditions of tripartite separability are also sufficient at W state side.

scholarly journals Entanglement distribution in pure-state quantum networks

2008 ◽  
Vol 77 (2) ◽  
Author(s):  
Sébastien Perseguers ◽  
J. Ignacio Cirac ◽  
Antonio Acín ◽  
Maciej Lewenstein ◽  
Jan Wehr
Keyword(s):  
Pure State ◽  
Quantum Networks ◽  
Entanglement Distribution

Generation of W state and GHZ state of multiple atomic ensembles via a single atom in a nonresonant cavity

2014 ◽  
Vol 312 ◽  
pp. 269-274 ◽  
Author(s):  
Chun-Ling Zhang ◽  
Wen-Zhang Li ◽  
Mei-Feng Chen
Keyword(s):  
Ghz State ◽  
W State ◽  
Single Atom ◽  
Atomic Ensembles

Effective protocol for preparation of three-atom Greenberger-Horne-Zeilinger state and W state with the help of cross-Kerr nonlinearity

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Yi-Hao Kang ◽  
Yan Xia ◽  
Pei-Min Lu
Keyword(s):  
Kerr Nonlinearity ◽  
Ghz State ◽  
W State ◽  
Quantum Nondemolition ◽  
Linear Elements

AbstractWe propose a protocol to generate a Greenberger-Horne-Zeilinger (GHZ) state andWstate by using simple linear elements and quantum nondemolition detectors (QNDs). With the help of cross-Kerr nonlinearity, our protocol can generate the intended states with only one setup, and the probability of getting a W state is greatly increased when compared with previous schemes [Phys. Rev. A 75 (2007) 044301]. Also, our proposed protocol is realizable in experiments.

Semi-quantum secret sharing protocol using W-state

2019 ◽  
Vol 34 (27) ◽  
pp. 1950213 ◽  
Author(s):  
Chia-Wei Tsai ◽  
Chun-Wei Yang ◽  
Narn-Yih Lee
Keyword(s):  
Secret Sharing ◽  
Bell State ◽  
Quantum Secret Sharing ◽  
Ghz State ◽  
W State ◽  
Important Research ◽  
Entanglement Property ◽  
Entanglement State ◽  
Entanglement States ◽  
Quantum Protocol

Quantum secret sharing protocol, which lets a master share a secret with his/her agents and the agents can recover the master’s secret when they collaborate, is an important research issue in the quantum information field. In order to make the quantum protocol more practical, the concept of semi-quantum protocol is advanced by Boyer et al. Based on this concept, many semi-quantum secret sharing protocols have been proposed. The various entanglement states (including Bell state, GHZ state and so on) were used to be the quantum resources in these SQSS protocols, except for W-state which is the other multi-qubit entanglement state and different from GHZ states. Therefore, this study wants to use the entanglement property of W-state to propose the first three-party SQSS protocol and analyze the proposed protocol is free from the well-known attacks.

ENTANGLEMENT DYNAMICS OF THREE-QUBIT STATES UNDER A SPIN ENVIRONMENT

2011 ◽  
Vol 09 (02) ◽  
pp. 791-800 ◽  
Author(s):  
XIAO SAN MA ◽  
GAO SHENG LIU ◽  
AN MIN WANG
Keyword(s):  
Coupling Strength ◽  
Degrees Of Freedom ◽  
Ghz State ◽  
W State ◽  
Matrix Elements ◽  
Entanglement Dynamics ◽  
Werner State ◽  
Qubit States ◽  
Decoherence Free Subspaces

In this paper, we investigate the entanglement dynamics of three-qubit states under a spin environment. From the analysis, we find that the entanglement dynamics of the three-qubit states depends not only on the coupling strength between the system and the environment and the number of degrees of freedom of the environment but also on the tunneling matrix elements of the spin environment and the specific state of concern. Specifically, the entanglement dynamics of the GHZ state, the W state, and the Werner state have been analyzed in detail and the conditions to identify the decoherence-free subspaces of our model have been discussed.

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