Distance-based approach to quantum coherence and nonclassicality

Abstract

We provide a coherence-based approach to nonclassical behavior by means of distance measures. We develop a quantitative relation between coherence and nonclassicality quantifiers, which establish the nonclassicality as the maximum quantum-coherence achievable. We compute the coherence of several representative examples and discuss whether the theory may be extended to reference observables with continuous spectra.

Beam splitter as quantum coherence-maker

“…In figure 7 it is represented the final coherence as a function of the parameter θ for different squeezing parameters ξ. The minimum coherence, at θ = 0 coincides with the coherence of the squeezed vacuum without any beam splitter transformation [19] ( )…”

“…In this work, we focus on characterizing one operation that is not free with regard to quantum coherence, the beam splitter (BS), which is able to enhance the coherence previously present in the system [18,19]. Beam splitters already display this behaviour of coherence-maker in classical optics, which makes them very intuitive to use in this quantum context and suitable for experimental implementations of coherence-based technologies [20][21][22].…”

Characterizing nonclassical correlation via local channels

“…Exploiting the above properties of entropic measure, we can prove that the Tsallis entropy is a bonafide measure of quantum coherence [24]. Further, for a specific value of α, the Tsallis α-relative entropy based coherence measure is related with the other coherence measures based on the relative entropy, Hilbert-Schmidt (HS) norm [51], Hellinger distance [52] and trace distance [15]. Further, the relation between the quantum discord and TαE coherence measure is also established recently [53].…”