Complementarity between quantum coherence and impurity: a majorization approach.

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

Buenos Arires

Conferencia; X Conference on Quantum Foundations (2021); 2021

Singh et al studied the bound imposed by mixedness of a quantum system on the amount of quantum coherence present in the system [1]. In particular, they found a nontrivial bound for the sum of coherence and mixedness measured with the l1-norm and the linear entropy, respectively. 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 general characteristic of quantum systems, regardless of the measures used. We study general quantifiers of coherence and impurity, namely: the generalized coherence vector introduced in [2] and the vector of eigenvalues, respectively. We observe the existence of a nontrivial bound for the tensor product between both vectors, which captures the trade-off between coherence and mixedness in general. Finally, we obtain the optimal bound in the case of a single-qubit system and a approximate numerical bound for the qutrit.[1] U. Singh, M. Nath Bera, H. S. Dhar, and A. K. Pati Phys. Rev.A 91, 052115 (2015).[2] G. M. Bosyk, M. Losada, C. Massri, H. Freytes and G. Sergioli Phys. Rev. A 103, 012403 (2021).G. M. Bosyk, G. Bellomo, F. Holik, H. Freytes and G. Sergioli. New J. Phys. 21, 083028 (2019)