2000 character limit reached
Almost all even-particle pure states are determined by their half-body marginals
Published 15 Jan 2024 in quant-ph | (2401.07499v1)
Abstract: Determining whether the original global state is uniquely determined by its local marginals is a prerequisite for some efficient tools for characterizing quantum states. This paper shows that almost all generic pure states of even $N$-particle with equal local dimension are uniquely determined among all other pure states (UDP) by four of their half-body marginals. Furthermore, we give a graphical description of the marginals for determining genuinely multipartite entangled states, which leads to several lower bounds on the number of required marginals. Finally, we present a construction of N-qudit states obtained from certain combinatorial structures that cannot be UDP by its k-body marginals for some k>N/2-1.
- A. A. Klyachko, “Quantum marginal problem and N𝑁Nitalic_N-representability,” Journal of Physics: Conference Series, vol. 36, no. 1, p. 72, 2006.
- C. Schilling, “The quantum marginal problem,” Mathematical Results in Quantum Mechanics: Proceedings of the QMath12 Conference, pp. 165–176, 2015.
- E. Haapasalo, T. Kraft, N. Miklin, and R. Uola, “Quantum marginal problem and incompatibility,” Quantum, vol. 5, p. 476, 2021.
- C. Schilling, “Quantum marginal problem and its physical relevance,” arXiv:1507.00299.
- T. Tyc and J. Vlach, “Quantum marginal problems,” The European Physical Journal D, vol. 69, 2015.
- A. J. Coleman, “Structure of Fermion Density Matrices,” Reviews of modern Physics, vol. 35, pp. 668–686, 1963.
- T. Xin, D. Lu, J. Klassen, N. Yu, Z. Ji, J. Chen, X. Ma, G. Long, B. Zeng, and R. Laflamme, “Quantum State Tomography via Reduced Density Matrices,” Phys. Rev. Lett., vol. 118, p. 020401, 2017.
- J. Cotler and F. Wilczek, “Quantum overlapping tomography,” Phys. Rev. Lett., vol. 124, p. 100401, 2020.
- N. Linden, S. Popescu, and W. K. Wootters, “Almost every pure state of three qubits is completely determined by its two-particle reduced density matrices,” Phys. Rev. Lett., vol. 89, p. 207901, 2002.
- S. N. Walck and D. W. Lyons, “Only n𝑛nitalic_n-qubit Greenberger-Horne-Zeilinger states are undetermined by their reduced density matrices,” Phys. Rev. Lett., vol. 100, p. 050501, 2008.
- S. N. Walck and D. W. Lyons, “Only n𝑛nitalic_n-qubit Greenberger-Horne-Zeilinger states contain n𝑛nitalic_n-partite information,” Phys. Rev. A, vol. 79, p. 032326, 2009.
- N. S. Jones and N. Linden, “Parts of quantum states,” Phys. Rev. A, vol. 71, p. 012324, 2005.
- S. Huang, J. Chen, Y. Li, and B. Zeng, “Quantum state tomography for generic pure states,” SCIENCE CHINA Physics, Mechanics &\&& Astronomy, vol. 61, no. 11, pp. 1–7, 2018.
- F. Huber and S. Severini, “Some Ulam’s reconstruction problems for quantum states,” Journal of Physics A: Mathematical and Theoretical, vol. 51, no. 43, p. 435301, 2018.
- B. Bollobás, “Almost every graph has reconstruction number three,” Journal of Graph Theory, vol. 14, no. 1, pp. 1–4, 1990.
- L. Diósi, “Three-party pure quantum states are determined by two two-party reduced states,” Phys. Rev. A, vol. 70, p. 010302, 2004.
- J. Chen, Z. Ji, M. B. Ruskai, B. Zeng, and D. Zhou, “Comment on some results of erdahl and the convex structure of reduced density matrices,” Journal of Mathematical Physics, vol. 53, no. 7, pp. 1608–1621, 2012.
- N. Wyderka, F. Huber, and O. Gühne, “Almost all four-particle pure states are determined by their two-body marginals,” Phys. Rev. A, vol. 96, p. 010102, 2017.
- S. Lloyd and H. Pagels, “Complexity as thermodynamic depth,” Annals of physics, vol. 188, no. 1, pp. 186–213, 1988.
- A. J. Scott and C. M. Caves, “Entangling power of the quantum baker’s map,” Journal of Physics A: Mathematical and General, vol. 36, no. 36, p. 9553, aug 2003.
- P. Parashar and S. Rana, “N𝑁Nitalic_N-qubit W𝑊Witalic_W states are determined by their bipartite marginals,” Phys. Rev. A, vol. 80, p. 012319, 2009.
- X. Wu, G. Tian, W. Huang, Q. Wen, S. Qin, and F. Gao, “Determination of W𝑊Witalic_W states equivalent under stochastic local operations and classical communication by their bipartite reduced density matrices with tree form,” Phys. Rev. A, vol. 90, p. 012317, 2014.
- S. Rana and P. Parashar, “Optimal reducibility of all w𝑤witalic_w states equivalent under stochastic local operations and classical communication,” Phys. Rev. A, vol. 84, p. 052331, 2011.
- X. Wu, Y. Yang, Q. Wen, S. Qin, and F. Gao, “Determination of Dicke states equivalent under stochastic local operations and classical communication,” Phys. Rev. A, vol. 92, p. 052338, 2015.
- L. Arnaud and N. J. Cerf, “Exploring pure quantum states with maximally mixed reductions,” Phys. Rev. A, vol. 87, p. 012319, 2013.
- D. Goyeneche, Z. Raissi, S. Di Martino, and K. Życzkowski, “Entanglement and quantum combinatorial designs,” Phys. Rev. A, vol. 97, p. 062326, 2018.
- D. Goyeneche and K. Życzkowski, “Genuinely multipartite entangled states and orthogonal arrays,” Phys. Rev. A, vol. 90, p. 022316, 2014.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.