Maximal lexicographic spectra and ranks for states with fixed uniform margins
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- by Xin Li
- Proc. Amer. Math. Soc. 147 (2019), 3303-3315
- DOI: https://doi.org/10.1090/proc/14494
- Published electronically: April 3, 2019
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Abstract:
We find the spectrum in maximal lexicographic order for quantum states $\rho _{AB}\in \mathcal {H}_A\otimes \mathcal {H}_B$ with margins $\rho _A=\frac {1}{n}I_n$ and $\rho _B=\frac {1}{m}I_m$ and discuss the construction of $\rho _{AB}$. By nonzero rectangular Kronecker coefficients, we give counterexamples for Klyachko’s conjecture which says that a quantum state with maximal lexicographical spectrum has minimal rank among all states with given margins. Moreover, we show that quantum states with the maximal lexicographical spectrum are extreme points.References
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Bibliographic Information
- Xin Li
- Affiliation: Department of Mathematics, Zhejiang University of Technology, Hangzhou 310023, People’s Republic of China
- Email: xinli1019@126.com
- Received by editor(s): January 8, 2018
- Received by editor(s) in revised form: November 7, 2018
- Published electronically: April 3, 2019
- Additional Notes: The research was supported by National Natural Science Foundation of China (Grant No.11626211).
- Communicated by: Pham Huu Tiep
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3303-3315
- MSC (2010): Primary 20C30; Secondary 15A18
- DOI: https://doi.org/10.1090/proc/14494
- MathSciNet review: 3981109