Partially unbiased entangled bases
Amir Kalev, F. C. Khanna, M. Revzen · Physical Review A · 2009
In this contribution we group the operator basis for ${d}^{2}$-dimensional Hilbert space in a way that enables us to relate bases of entangled states with single-particle mutually unbiased state bases (MUB), each in dimensionality $d$. We utilize these sets of operators to show that an arbitrary density matrix for this ${d}^{2}$-dimensional Hilbert-space system is analyzed via ${d}^{2}+d+1$ measurements, ${d}^{2}\ensuremath{-}d$ of which involve those entangled states that we associate with MUB of the $d$-dimensional single-particle constituents. The number ${d}^{2}+d+1$ lies in the middle of the number of measurements needed for bipartite state reconstruction with two-particle MUB $({d}^{2}+1)$ and those needed by single-particle MUB $[{({d}^{2}+1)}^{2}]$.