High-dimensional encoding of quantum information provides a way of transcending the
limitations of current approaches to quantum communication, which are mostly based on the …

Uncertainty relations involving incompatible observables are one of the cornerstones of
quantum mechanics. Aside from their fundamental significance, they play an important role …

Quantum measurements based on mutually unbiased bases are commonly used in
quantum information processing, as they are generally viewed as being maximally …

We derive a framework for quantifying entanglement in multipartite and high dimensional
systems using only correlations in two unbiased bases. We furthermore develop such …

Sum and product uncertainty relations, containing variances of three or four observables, but
not containing explicitly their covariances, are derived. Their consequences are, in …

The notion of mutual unbiasedness for coarse-grained measurements of quantum
continuous variable systems is considered. It is shown that while the procedure of “standard” …

Partially coherent optical beams present phenomena that may not appear in perfectly
coherent beams. In this regard, spontaneous parametric downconversion is an intriguing …

Majorization uncertainty relations are generalized for an arbitrary mixed quantum state ρ of a
finite size N. In particular, a lower bound for the sum of two entropies characterizing the …

For a quantum particle with a single degree of freedom, we derive preparational sum and
product uncertainty relations satisfied by N linear combinations of position and momentum …

Mutual unbiasedness of the eigenstates of phase-space operators—such as position and
momentum, or their standard coarse-grained versions—exists only in the limiting case of …