Quantifying the Coherence between Coherent States

Abstract

In this Letter, we detail an orthogonalization procedure that allows for the quantification of the amount of coherence present in an arbitrary superposition of coherent states. The present construction is based on the quantum coherence resource theory introduced by Baumgratz, Cramer, and Plenio and the coherence resource monotone that we identify is found to characterize the nonclassicality traditionally analyzed via the Glauber-Sudarshan P distribution. This suggests that identical quantum resources underlie both quantum coherence in the discrete finite dimensional case and the nonclassicality of quantum light. We show that our construction belongs to a family of resource monotones within the framework of a resource theory of linear optics, thus establishing deeper connections between the class of incoherent operations in the finite dimensional regime and linear optical operations in the continuous variable regime.

Converting multilevel nonclassicality into genuine multipartite entanglement

“…This reveals a qualitative and quantitative connection between multilevel nonclassicality and multipartite entanglement, generalizing previous results in the resource theory of quantum coherence [7,12,26], and further contributing towards the formalization of nonclassicality as a resource [15,16,31,32,63]. In particular, multilevel coherence and multipartite entanglement provide significant operational advantages over the resources of standard quantum coherence and bipartite entanglement [13,54,64] and are key ingredients for practical applications such as quantum computation, quantum networks, sensing, and metrology [64][65][66][67].…”

“…The quantitative interplay between the degree of nonclassicality and the bipartite entanglement obtained from it has been investigated as well [15,16,20,[24][25][26][27]. These studies have advanced our understanding of nonclassicality as a resource in systems of arbitrary dimension [7,12,15,16,[28][29][30][31][32].…”

Operational Resource Theory of Continuous-Variable Nonclassicality

“…Here, building on the approach of Ref. [52], we choose the free states to coincide with the set C n of classical states on n modes, consisting of convex mixtures of coherent states. In terms of the Glauber-Sudarshan Pfunction, we have…”

“…They have been instrumental in understanding quantum reference frames [30], thermodynamics [31][32][33][34], coherence [35][36][37], contextuality [38], steering [39], and non-Gaussianity [40][41][42][43]. Resourcetheoretic terminology in continuous variables has appeared in a number of recent works [44][45][46][47][48][49][50][51][52], but these ideas are still in their infancy.…”

Optimizing nontrivial quantum observables using coherence

“…Some known measures include geometric measures [2], the robustness of coherence [6][7][8], and entanglement based measures [9]. Coherence measures have now been studied in relation to a diverse range of quantum effects such as quantum interference [10], exponential speed-up in quantum algorithms [11,12] and quantum metrology [13,14], nonclassical light [15][16][17], quantum macroscopicity [18,19] and quantum correlations [20][21][22][23][24][25]. An overview of coherence measures and their structure may be found in [26,27].…”