Abstract
We consider local unitary transformations acting on a multiparty symmetric pure state and determine the stabilizer dimension of any pure symmetric state.
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Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)
Linden, N., Popescu, S.: On multi-particle entanglement. Fortschr. Phys. 46, 567 (1998)
Linden, N., Popescu, S., Sudbery, A.: Non-local properties of multi-particle density matrices. Phys. Rev. Lett. 83, 243 (1999)
Carteret, H.A., Sudbery, A.: Local symmetry properties of pure 3-qubit states. J. Phys. A 33, 4981 (2000)
Sudbery, A.: On local invariants of pure three-qubit states. J. Phys. A 34, 643 (2001)
Makhlin, Yu.: Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations. Quantum Inf. Process. 1, 243 (2002)
Lyons, D.W., Walck, S.N.: Minimum orbit dimension for local unitary action on n-qubit pure states. J. Math. Phys. 46, 102106 (2005)
Lyons, D.W., Walck, S.N.: Classification of n-qubit states with minimum orbit dimension. J. Phys. A 39, 2443 (2006)
Lyons, D.W., Walck, S.N.: Maximum stabilizer dimension for nonproduct states. Phys. Rev. A 76, 022303 (2007)
Lyons, D.W., Walck, S.N., Blanda, S.A.: Classification of nonproduct states with maximum stabilizer dimension. Phys. Rev. A 77, 022309 (2008)
Lyons, D.W., Walck, S.N.: Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group. Phys. Rev. A 78, 042314 (2008)
Zhang, D.H., Fan, H., Zhou, D.L.: Stabilizer dimension of graph states. Phys. Rev. A 79, 042318 (2009)
Stockton, J.K., Geremia, J.M., Doherty, A.C., Mabuchi, H.: Characterizing the entanglement of symmetric many-particle spin-1 2 systems. Phys. Rev. A 67, 022112 (2003)
Bastin, T., Krins, S., Mathonet, P., Godefroid, M., Solano, E.: Operational families of entanglement classes for symmetric n-qubit states. Phys. Rev. Lett. 103, 070503 (2009)
Mathonet, P., Krins, S., Godefroid, M., Solano, E., Bastin, T.: Entanglement equivalence of n-qubit symmetric states. Phys. Rev. A 81, 052315 (2010)
Lyons, D.W., Walck, S.N.: Entanglement classes of symmetric Werner states. Phys. Rev. A 84, 042316 (2011)
Lyons, D.W., Skelton, A.M., Walck, S.N.: Werner state structure and entanglement classification. Adv. Math. Phys. 1, 463610 (2012)
Lyons, D.W., Walck, S.N.: Symmetric mixed states of n qubits: local unitary stabilizers and entanglement classes. Phys. Rev. A 84, 042340 (2011)
Acknowledgements
The authors thank Professor Shaoming Fei for his advice. Bo Li is supported by Natural Science Foundation of China (Grants No. 11305105), the Natural Science Foundation of Jiangxi Province (Grants No. 20132BAB212010). Jiao-jiao Li is supported by Youth Foundation of Henan Normal University (12QK02) and Zhixi Wang is supported by KZ201210028032.
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Li, B., Li, J. & Wang, Z. The Stabilizer Dimension of n-Qubit Symmetric States. Int J Theor Phys 53, 612–621 (2014). https://doi.org/10.1007/s10773-013-1847-1
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DOI: https://doi.org/10.1007/s10773-013-1847-1