Mixtures of coherent states are commonly regarded as classical. Here we show that there is a quantum advantage in discriminating between coherent states in a mixture, implying the presence of quantum properties in the mixture, which are however not captured by commonly used non-classicality measures. We identify a set of desired properties for any non-classicality measure that aims to capture these quantum features, and define the discord potential CD, which we show to satisfy all those properties. We compare the discord potential with recently proposed coherence monotones, and prove that the coherence monotones diverge for classically distinguishable states, thus indicating their failure to quantify non-classicality in this limit. On the technical side, we provide a simple method of calculating the discord as well as other information-theoretic quantities for the (non-Gaussian) output of any input state with positive P-function.
We consider two celebrated criteria for defining the nonclassicality of bipartite bosonic quantum systems, the first stemming from information theoretic concepts and the second from physical constraints on the quantum phase space. Consequently, two sets of allegedly classical states are singled out: (i) the set C composed of the so-called classical-classical (CC) states-separable states that are locally distinguishable and do not possess quantum discord; (ii) the set P of states endowed with a positive P representation (P-classical states)-mixtures of Glauber coherent states that, e.g., fail to show negativity of their Wigner function. By showing that C and P are almost disjoint, we prove that the two defining criteria are maximally inequivalent. Thus, the notions of classicality that they put forward are radically different. In particular, generic CC states show quantumness in their P representation, and vice versa, almost all P-classical states have positive quantum discord and, hence, are not CC. This inequivalence is further elucidated considering different applications of P-classical and CC states. Our results suggest that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.
A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan
P function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify the nonclassicality of a single qubit, defined by the vacuum and single-photon states, by applying the following four well-known measures of nonclassicality: (1) the nonclassical depth, $\ensuremath{\tau}$, related to the minimal amount of Gaussian noise which changes a nonpositive
P function into a positive one; (2) the nonclassical distance
D, defined as the Bures distance of a given state to the closest classical state, which is the vacuum for the single-qubit Hilbert space; together with (3) the negativity potential (NP), and (4) concurrence potential, which are the nonclassicality measures corresponding to the entanglement measures (i.e., the negativity and concurrence, respectively) for the state generated by mixing a single-qubit state with the vacuum on a balanced beam splitter. We show that complete statistical mixtures of the vacuum and single-photon states are the most nonclassical single-qubit states regarding the distance
D for a fixed value of both the depth $\ensuremath{\tau}$ and NP in the whole range
[0,1] of their values, as well as the NP for a given value of $\ensuremath{\tau}$ such that $\ensuremath{\tau}>0.315\phantom{\rule{0.16em}{0ex}}4$. Conversely, pure states are the most nonclassical single-qubit states with respect to $\ensuremath{\tau}$ for a given
D, NP versus
D, and $\ensuremath{\tau}$ versus NP. We also show the ``relativity'' of these nonclassicality measures by comparing pairs of single-qubit states: if a state is less nonclassical than another state according to some measure then it might be more nonclassical according to another measure. Moreover, we find that the concurrence potential is equal to the nonclassical distance for single-qubit states. This implies an operational interpretation of the nonclassical distance as the potential for the entanglement of formation.
One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.
Consider two bosonic modes which are prepared in one of two possible Gaussian states with the same local energy: either a tensor-product thermal state (with zero correlations) or a separable Gaussian state with maximal correlations (with both classical and quantum correlations, the latter being quantified by quantum discord). For the discrimination of these states, we compare the optimal joint coherent measurement with the best local measurement based on single-mode Gaussian detections. We show how the coherent measurement always strictly outperforms the local detection strategy for both single- and multi-copy discrimination. This means that using local Gaussian measurements (assisted by classical communication) is strictly suboptimal in detecting discord. A better performance may only be achieved by either using non Gaussian measurements (non linear optics) or coherent non-local measurements.
We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.
We study theoretically how multiple scattering of light in a disordered medium can spontaneously generate quantum correlations. In particular we focus on the case where the input state is Gaussian and characterize the correlations between two arbitrary output modes. As there is not a single all-inclusive measure of correlation, we characterise the output correlations with three measures: intensity fluctuations, entanglement, and quantum discord. We find that, while a coherent input state can not produce quantum correlations, any other Gaussian input will produce them in one form or another. This includes input states that are usually regarded as more classical than coherent ones, such as thermal states, which will produce a non-zero quantum discord.