Quantum coherence: Reciprocity and distribution

Abstract

Quantum coherence is the outcome of the superposition principle. Recently, it has been theorized as a quantum resource, and is the premise of quantum correlations in multipartite systems. It is therefore interesting to study the coherence content and its distribution in a multipartite quantum system. In this work, we show analytically as well as numerically the reciprocity between coherence and mixedness of a quantum state. We find that this trade-off is a general feature in the sense that it is true for large spectra of measures of coherence and of mixedness. We also study the distribution of coherence in multipartite systems by looking at monogamytype relation-which we refer to as additivity relation-between coherences of different parts of the system. We show that for the Dicke states, while the normalized measures of coherence violate the additivity relation, the unnormalized ones satisfy the same.

Colloquium: Quantum coherence as a resource

“…As was shown in (Kumar, 2017;Yao et al, 2015), the relative entropy of coherence is not monogamous in general, although it can be monogamous for certain families of states. Further results on monogamy of coherence have also been presented by (Radhakrishnan et al, 2016).…”

“…For a d-dimensional system and any fixed spectrum {p n } d n=1 , (Streltsov et al, 2016b) have proven that the state max = d n=1 p n |n + n + |, where {|n + } denotes a mutually unbiased basis with respect to the incoherent basis {|i } (that is, | i|n + | 2 = 1 d ), is a universal maximally coherent mixed state with respect to any coherence monotone under the set MIO. Complementarity relations between measures of purity and coherence have been further investigated in (Cheng and Hall, 2015;Giorda and Allegra, 2016a;Kumar, 2017;Streltsov et al, 2016b;Xi et al, 2015b).…”

“…, is a universal maximally coherent mixed state with respect to any coherence monotone under the set MIO. Complementarity relations between measures of purity and coherence have been further investigated in (Cheng and Hall, 2015;Giorda and Allegra, 2016a;Kumar, 2017;Streltsov et al, 2016b;Xi et al, 2015b).…”

Hallmarking quantum states: unified framework for coherence and correlations

“…As mentioned in the introduction, the distribution of coherence in multipartite settings has been subject of recent interest [32,33,34,35]. Building on these results, it is useful to introduce the concept of local coherence that is present in the state π π π( ) to be distinguished from genuine multipartite effects [32,35].…”

“…Coherence has also been linked to asymmetry [22,23,24] and purity [25]. The interplay between quantum correlations and coherence is mainly studied focusing on either the problem of interconversion between the two classes of resources [26,27,28,29,30] or the distribution of coherence among subparties and its monogamy properties [31,32,33,34,35,36].…”