Structure of the density matrix providing the minimum of generalized uncertainty relation for mixed states
arXiv:quant-ph/0006055 · doi:10.1088/0305-4470/33/38/311
Abstract
For configurational space of arbitrary dimension a strict form of the uncertainty principle has been obtained, which takes into account the dependence of inequality limit on the effective number of pure states present in given statistical mixture. It is shown that in a state with minimal uncertainty the density operators eigenfunctions coincide with the stationary wavefunctions of a multidimensional harmonic oscillator. The mixed state obtained has a permutational symmetry which is typical for a system of identical bosons.
11 pages, 3 figures, LaTeX 2e with IOP format file (included), submitted to J. Phys. A, also was presented at International Conference on Quantum Optics (Raubichi, Belarus, May 28-31, 2000)