A new coherence measure based on fidelity

Abstract

Quantifying coherence is an essential endeavor for both quantum foundations and quantum technologies. In this paper, we put forward a quantitative measure of coherence by following the axiomatic definition of coherence measures introduced in [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. Our measure is based on fidelity and analytically computable for arbitrary states of a qubit. As one of its applications, we show that our measure can be used to examine whether a pure qubit state can be transformed into another pure or mixed qubit state only by incoherent operations.Comment: 10 page

Influence of Stark-shift on quantum coherence and non-classical correlations for two two-level atoms interacting with a single-mode cavity field

“…The Baumgratz et al analysis [51] has attracted deep attention of many researchers and various measures of QC, which satisfy the physical requirements of noncontractivity and monotonicity, have been proposed since then. We quote, for instance, the l 1 -norm coherence [51], the coherence of formation [58,59], the relative entropy coherence [51], the geometric measure of coherence [60], the distillable coherence [59,61], the coherence measures based on entanglement [60,62], the coherence measures based on trace norm [58], the coherence measure via quantum skew information [63], via Tsallis relative entropy [64,65], via fidelity [66] and via relative entropy in Gaussian states [67].…”

Existence of maximally correlated states

“…A measure satisfying this requirement is called entanglement monotone. Similar monotones have been defined for other quantum resources, such as nonuniformity, coherence, or asymmetry [9][10][11][12][13][14][15][16].…”

“…Note that here the codomains of the local operators K q,s and K q ′ ,s ′ can be different from one another provided q ′ = q. A very commun requirement for measures of entanglement or of any quantum resource [1,8,[10][11][12][13][14][15][16] reads here as follows. Condition 2.…”

The Tightness of Multipartite Coherence from Spectrum Estimation

“…Based on the general framework, several coherence measures have been proposed, such as the l 1 norm of coherence, the relative entropy of coherence [12], the geometric measure of coherence [17], the robustness of coherence [19,20], some convex roof quantifiers of coherence [21][22][23][24][25], and others [26][27][28][29][30][31][32]. These coherence measures make it possible to quantify the role of coherence in different quantum information processing tasks, especially in the multipartite scenario, such as quantum state merging [33], coherence of assistance [34], incoherent teleportation [35], coherence localization [36], and anti-noise quantum metrology [37].…”