@unpublished{55560, abstract = {{Non-symmetric GHZ states ($n$-GHZ$_\alpha$), characterized by unequal superpositions of $|00...0>$ and $|11...1>$, represent a significant yet underexplored class of multipartite entangled states with potential applications in quantum information. Despite their importance, the lack of a well-defined stabilizer formalism and corresponding graph representation has hindered their comprehensive study. In this paper, we address this gap by introducing two novel graph formalisms and stabilizers for non-symmetric GHZ states. First, we provide a weighted hypergraph representation and demonstrate that non-symmetric GHZ states are local unitary (LU) equivalent to fully connected weighted hypergraphs. Although these weighted hypergraphs are not stabilizer states, we show that they can be stabilized using local operations, and an ancilla. We further extend this framework to qudits, offering a specific form for non-symmetric qudit GHZ states and their LU equivalent weighted qudit hypergraphs. Second, we propose a graph formalism using controlled-unitary (CU) operations, showing that non-symmetric qudit GHZ states can be described using star-shaped CU graphs. Our findings enhance the understanding of non-symmetric GHZ states and their potential applications in quantum information science.}}, author = {{Zakaryan, Hrachya and Revis, Konstantinos-Rafail and Raissi, Zahra}}, booktitle = {{arXiv:2408.02740}}, title = {{{Non-symmetric GHZ states; weighted hypergraph and controlled-unitary graph representations}}}, year = {{2024}}, } @unpublished{55657, abstract = {{Graph states are a class of multi-partite entangled quantum states, where colorability, a property rooted in their mathematical foundation, has significant implications for quantum information processing. In this study, we investigate the colorability of graph states in qudit systems to simplify their representation and enhance their practical applications. We present closed-form expressions for all two-colorable graph states. Our findings show that the closed-form expression of these states is tightly linked to the graph structure and the distribution of particles in red ($n_R$) and blue ($n_B$). Additionally, we explore a broad family of three-colorable graph states constructed from two two-colorable graph states. The closed-form expression for these states is in the form of one two-colorable state tensor product with the graph basis formed from another two-colorable state. Our approach systematically reduces the number of terms required to represent these states. Furthermore, we demonstrate that many well-known mathematical graphs, including friendship graphs, fit within our formalism. Finally, we discuss the LU/SLOCC (Local Unitary/Stochastic Local Operation and Classical Communication) equivalence between two- and three-colorable graph states. Our findings have broad implications for characterizing the LU/SLOCC equivalence of graph state classes and pave the way for future research.}}, author = {{Revis, Konstantinos-Rafail and Zakaryan, Hrachya and Raissi, Zahra}}, booktitle = {{arXiv:2408.09515}}, title = {{{Closed-Form Expressions for Two- and Three-Colorable States}}}, year = {{2024}}, } @article{55521, author = {{Frantzeskakis, Rafail and Liu, Chenxu and Raissi, Zahra and Barnes, Edwin and Economou, Sophia E.}}, issn = {{2643-1564}}, journal = {{Physical Review Research}}, number = {{2}}, publisher = {{American Physical Society (APS)}}, title = {{{Extracting perfect GHZ states from imperfect weighted graph states via entanglement concentration}}}, doi = {{10.1103/physrevresearch.5.023124}}, volume = {{5}}, year = {{2023}}, } @article{55522, author = {{Raissi, Zahra and Burchardt, Adam and Barnes, Edwin}}, issn = {{2469-9926}}, journal = {{Physical Review A}}, number = {{6}}, publisher = {{American Physical Society (APS)}}, title = {{{General stabilizer approach for constructing highly entangled graph states}}}, doi = {{10.1103/physreva.106.062424}}, volume = {{106}}, year = {{2022}}, } @article{55525, author = {{Raissi, Zahra and Teixidó, Adam and Gogolin, Christian and Acín, Antonio}}, issn = {{2643-1564}}, journal = {{Physical Review Research}}, number = {{3}}, publisher = {{American Physical Society (APS)}}, title = {{{Constructions of k-uniform and absolutely maximally entangled states beyond maximum distance codes}}}, doi = {{10.1103/physrevresearch.2.033411}}, volume = {{2}}, year = {{2020}}, } @article{55524, author = {{Burchardt, Adam and Raissi, Zahra}}, issn = {{2469-9926}}, journal = {{Physical Review A}}, number = {{2}}, publisher = {{American Physical Society (APS)}}, title = {{{Stochastic local operations with classical communication of absolutely maximally entangled states}}}, doi = {{10.1103/physreva.102.022413}}, volume = {{102}}, year = {{2020}}, } @article{55523, author = {{Raissi, Zahra}}, issn = {{2169-3536}}, journal = {{IEEE Access}}, pages = {{222439--222448}}, publisher = {{Institute of Electrical and Electronics Engineers (IEEE)}}, title = {{{Modifying Method of Constructing Quantum Codes From Highly Entangled States}}}, doi = {{10.1109/access.2020.3043401}}, volume = {{8}}, year = {{2020}}, } @article{55526, author = {{Goyeneche, Dardo and Raissi, Zahra and Di Martino, Sara and Życzkowski, Karol}}, issn = {{2469-9926}}, journal = {{Physical Review A}}, number = {{6}}, publisher = {{American Physical Society (APS)}}, title = {{{Entanglement and quantum combinatorial designs}}}, doi = {{10.1103/physreva.97.062326}}, volume = {{97}}, year = {{2018}}, } @article{55527, author = {{Raissi, Zahra and Gogolin, Christian and Riera, Arnau and Acín, Antonio}}, issn = {{1751-8113}}, journal = {{Journal of Physics A: Mathematical and Theoretical}}, number = {{7}}, publisher = {{IOP Publishing}}, title = {{{Optimal quantum error correcting codes from absolutely maximally entangled states}}}, doi = {{10.1088/1751-8121/aaa151}}, volume = {{51}}, year = {{2017}}, } @article{55529, author = {{Raissi, Zahra and Karimipour, Vahid}}, issn = {{1570-0755}}, journal = {{Quantum Information Processing}}, number = {{3}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Creating maximally entangled states by gluing}}}, doi = {{10.1007/s11128-017-1535-9}}, volume = {{16}}, year = {{2017}}, } @article{55528, author = {{Johansson, Markus and Raissi, Zahra}}, issn = {{2469-9926}}, journal = {{Physical Review A}}, number = {{4}}, publisher = {{American Physical Society (APS)}}, title = {{{Constructing entanglement measures for fermions}}}, doi = {{10.1103/physreva.94.042319}}, volume = {{94}}, year = {{2016}}, } @article{55530, author = {{Zare, Somayeh and Raissi, Zahra and Mohammadzadeh, Hosein and Mirza, Behrouz}}, issn = {{1434-6044}}, journal = {{The European Physical Journal C}}, number = {{9}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Condensation of an ideal gas with intermediate statistics on the horizon}}}, doi = {{10.1140/epjc/s10052-012-2152-5}}, volume = {{72}}, year = {{2012}}, }