Coherence-impurity complementarity for quantum systems using entropies and majorization

MARIELA PORTESI; YANET ALVAREZ; MARCELO LOSADA; GUSTAVO MARTÍN BOSYK

Paris

Conferencia; 41st MaxEnt2022 Conference; 2022

Société de l'Electricité, de l'Electronique et des Technologies de l'Information et de la Communication (SEE)

Singh et al. studied the bound imposed by mixedness on the amount ofquantum coherence present in a quantum system. In particular, theyfound a nontrivial bound for the sum of coherence and mixedness whenthey are given, respectively, by the L1-norm and the linear entropy.Moreover, they showed a trade-off between the relative entropy of coherence and von Neumann entropy. Based on those results,coherence-impurity complementarity is expected to be a generalcharacteristic of quantum systems, regardless of the measures used.We study general quantiuers of coherence and impurity, namely: thegeneralized coherence vector and the vector of eigenvalues,respectively. We observe the existence of a nontrivial bound for thetensor product between both vectors, which captures the trade-offbetween coherence and mixedness in general. In particular we obtainthe optimal bound in the case of a single-qubit system, andapproximate numerical bounds for the qutrit and for dimension 4.p { line-height: 115%; margin-bottom: 0.25cm; background: transparent }