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The compositional structure of multipartite quantum entanglement [article]

Bob Coecke, Aleks Kissinger
2010 arXiv   pre-print
While multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols, obtaining a high-level, structural understanding of entanglement involving arbitrarily many  ...  In turn, this structure yields a compositional graphical model for expressing general multipartite states.  ...  We also show that GHZ-states and W-states play a foundational role in the composition of multipartite entangled states.  ... 
arXiv:1002.2540v2 fatcat:o4n66silbrezbjhepal537qsaq

Multipartite Entanglement Generation in a Structured Environment

Shijiao Wang, Xiao San Ma, Mu-Tian Cheng
2020 Entropy  
With analysis, we can find that the steady multipartite entanglement with different values can be generated after a long-time evolution for different sizes of the quantum system.  ...  Meanwhile, the couplings between the additional harmonic oscillators and the decay rate of additional harmonic oscillators have almost no effect on the multipartite entanglement generation.  ...  Through calculation, we get the linear entropy of the n-qubit quantum states by tracing the degrees of freedom of the structured environment off the composite state in Equation (5) in the following expression  ... 
doi:10.3390/e22020191 pmid:33285966 pmcid:PMC7516616 fatcat:3bk3evxhajefxlhwl52cwxfgb4

Compatibility conditions from multipartite entanglement measures

Jian-Ming Cai, Zheng-Wei Zhou, Shun Zhang, Guang-Can Guo
2007 Physical Review A. Atomic, Molecular, and Optical Physics  
Our results are tightly connected with the measures of multipartite entanglement.  ...  . ⊗ d_N composite quantum system and find necessary conditions for general m-party subsystem states to be the reduced states of a common N-party state.  ...  This work was funded by National Fundamental Research Program, NCET-04-0587, the Innovation funds from Chinese Academy of Sciences, and National Natural Science Foundation of China (Grant No. 60121503,  ... 
doi:10.1103/physreva.75.052324 fatcat:t6xxkl4mprfpfcq3m7nxzns5yq

Multipartite Entanglement in a Discrete Magnetic Bands Magnetic Lattice [article]

A. Abdelrahman, P. Hannaford, M. Vasiliev, K. Alameh
2009 arXiv   pre-print
The confinement of the coupled magnetic quantum well (CMQW) system may significantly improve the condition for the long-range entanglement of the multipartite (multi-qubits) to be used in quantum information  ...  Using magneto-optical materials, an asymmetric multi-quantum state magnetic lattice is proposed to host an entangled multipartite system formed by using a quantum degenerate gas of ultracold atoms in a  ...  However there are some theoretical frames considered to partially quantify the entanglement of composite quantum states, such as the entanglement distillation method [6] .  ... 
arXiv:0909.3433v1 fatcat:px4rszpjh5epzpzooxggd5bqde

Measure of genuine multipartite entanglement with computable lower bounds

Zhi-Hao Ma, Zhi-Hua Chen, Jing-Ling Chen, Christoph Spengler, Andreas Gabriel, Marcus Huber
2011 Physical Review A. Atomic, Molecular, and Optical Physics  
We introduce an intuitive measure of genuine multipartite entanglement which is based on the well-known concurrence.  ...  These lower bounds are experimentally implementable in a feasible way enabling quantification of multipartite entanglement in a broad variety of cases.  ...  A measure of genuine multipartite entanglement FIG. 1: Illustration of the convex nested structure of multipartite entanglement.  ... 
doi:10.1103/physreva.83.062325 fatcat:22kh2eibm5gblpcxhgm4uad6qa

Operational Interpretation for Global Multipartite Entanglement

S. Boixo, A. Monras
2008 Physical Review Letters  
We show that the estimation of the strength of low-noise locally depolarizing channels, as quantified by the regularized quantum Fisher information, is directly related to the Meyer-Wallach multipartite  ...  We introduce an operational interpretation for pure-state global multipartite entanglement based on quantum estimation.  ...  We introduce an operational interpretation for pure-state global multipartite entanglement based on quantum estimation.  ... 
doi:10.1103/physrevlett.100.100503 pmid:18352168 fatcat:on6hu4gywfb4pg3j55u3nu6jwq

Entanglement measure for any quantum states [article]

Hyuk-jae Lee, Sung Dahm Oh, Doyeol Ahn
2003 arXiv   pre-print
The entanglement measure for multiqudits is proposed. This measure calculates the partial entanglement distributed by subsystems and the complete entanglement of the total system.  ...  This shows that we need to measure the subsystem entanglements to explain the full description for multiqudit entanglement.  ...  Our measure gives full description on the entanglement structure to the given composite quantum systems.  ... 
arXiv:quant-ph/0306127v1 fatcat:6gzboy7rvrhlpfemitprpddmum

Quantum state concentration and classification of multipartite entanglement

S. M. Zangi, Jun-Li Li, Cong-Feng Qiao
2018 Physical Review A  
The results not only simplify the tedious work of verifying the (in)equivalence of multipartite entangled states, but also are instructive to the quantum many-body problem involving multipartite entanglement  ...  Here we introduce a quantum state concentration scheme which decomposes the multipartite entangled state into a set of bipartite and tripartite entangled states.  ...  This concentration of multipartite entanglement to core entanglements has a similar structure as that of the tree tensor network state [15] , and when applying to entanglement classification we find:  ... 
doi:10.1103/physreva.97.012301 fatcat:d4pcj2las5fzfkubftouruc3ke

Entanglement Theory and a q Analogue Entangled State

Huihui Zhang, Abdul Rauf, Xiaoguang Zhou
2007 PIERS Online  
It exhibits a much richer structure than ordinary bipartite entanglement. Thus there will be abundant information in the quantum teleportation.  ...  Entangled state and entanglement theory in the quantum information are presented. A q analogue entangled state is first put forward in this paper.  ...  In the other words, for any composite quantum systems the existence of the EW denotes the presence of entanglement.  ... 
doi:10.2529/piers060906095324 fatcat:v5w4hllrgjaobk7zphckzsmw5q

Combinatory-Algebraic Perspective on Multipartiteness, Entanglement and Quantum Localization

Ioannis Raptis, Romàn R. Zapatrin
2005 International Journal of Theoretical Physics  
We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states  ...  In a more general setting, to capture the relativity and variability of our structures with respect to the observation means, sheaves of algebras may need be introduced.  ...  the full fledged multipartite structure of compound quantum systems.  ... 
doi:10.1007/s10773-005-7063-x fatcat:kctr5mwlnraxtdx3h2dmiqrbea

A Combinatory-Algebraic Perspective on Multipartiteness, Entanglement and Quantum Localization [article]

Ioannis Raptis, Roman Zapatrin
2002 arXiv   pre-print
We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states  ...  In a more general setting, to capture the relativity and variability of our structures with respect to the observation means, sheaves of algebras may need be introduced.  ...  the full fledged multipartite structure of compound quantum systems.  ... 
arXiv:quant-ph/0211077v1 fatcat:mh7ujwvp6jgltox4tlztyl5hte

General multipartite entangled states and complex projective variety [article]

Hoshang Heydari
2007 arXiv   pre-print
We discuss and investigate the geometrical structure of general multipartite states.  ...  In particular, we show that a geometrical measure of entanglement for general multipartite states can be constructed by the complex projective varieties defined by quadratic polynomials.  ...  Acknowledgments: The author acknowledges the financial support of the Japan Society for the Promotion of Science (JSPS).  ... 
arXiv:0708.2964v1 fatcat:ftdoebubcrdbvm7uutdbrxbuhq

Entanglement monogamy and entanglement evolution in multipartite systems

Yan-Kui Bai, Ming-Yong Ye, Z. D. Wang
2009 Physical Review A. Atomic, Molecular, and Optical Physics  
We analyze the entanglement distribution and the two-qubit residual entanglement in multipartite systems.  ...  For a composite system consisting of two cavities interacting with independent reservoirs, it is revealed that the entanglement evolution is restricted by an entanglement monogamy relation derived here  ...  Since the square of the concurrence is a good entanglement measure for two-qubit quantum state, the nonzero residual entanglement M A i A i Ј implies the existence of multipartite entanglement.  ... 
doi:10.1103/physreva.80.044301 fatcat:74ftpik5nfcmhmtln4w5vyorf4

Dissociation and annihilation of multipartite entanglement structure in dissipative quantum dynamics

Sergey N. Filippov, Alexey A. Melnikov, Mário Ziman
2013 Physical Review A. Atomic, Molecular, and Optical Physics  
We study the dynamics of the entanglement structure of a multipartite system experiencing a dissipative evolution.  ...  We also analyze the definitive phase of evolution when the annihilation of the entanglement compound finally takes place.  ...  INTRODUCTION The physical phenomenon of entanglement naturally appears in composite quantum systems via interactions among constituents.  ... 
doi:10.1103/physreva.88.062328 fatcat:74zf5twfo5dorkoc6fzm6nhqve

Quantum entanglement and symmetry

D Chruściński, A Kossakowski
2007 Journal of Physics, Conference Series  
One of the main problem in Quantum Information Theory is to test whether a given state of a composite quantum system is entangled or separable.  ...  We analyze multipartite invariant states and the corresponding symmetric quantum channels.  ...  Acknowledgments This work was partially supported by the Polish Ministry of Science and Higher Education Grant No 3004/B/H03/2007/33.  ... 
doi:10.1088/1742-6596/87/1/012008 fatcat:kcque264knf2xlv63dq4nue5ae
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