Proof of Sarkar-Kumar's Conjectures on Average Entanglement Entropies over the Bures-Hall Ensemble

@article{Wei2020ProofOS,
  title={Proof of Sarkar-Kumar's Conjectures on Average Entanglement Entropies over the Bures-Hall Ensemble},
  author={Lu Wei},
  journal={ArXiv},
  year={2020},
  volume={abs/2002.04085}
}
  • Lu Wei
  • Published 10 February 2020
  • Mathematics
  • ArXiv
Sarkar and Kumar recently conjectured [J. Phys. A: Math. Theor. $\textbf{52}$, 295203 (2019)] that for a bipartite system of Hilbert dimension $mn$, the mean values of quantum purity and von Neumann entropy of a subsystem of dimension $m\leq n$ over the Bures-Hall measure are given by \begin{equation*} \frac{2n(2n+m)-m^{2}+1}{2n(2mn-m^2+2)} \end{equation*} and \begin{equation*} \psi_{0}\left(mn-\frac{m^2}{2}+1\right)-\psi_{0}\left(n+\frac{1}{2}\right), \end{equation*} respectively, where $\psi_… 
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