Resources of the advantage in quantum Illumination: Discord and entanglement

Abstract

We investigate the quantum advantage in quantum illumination using two-qubit mixed states as the initial resource. We show that in quantum illumination, the achievable advantage is determined by an interplay between initial entanglement and discord. First, we rigorously show that the quantum advantage for a given state equals the amount of discord consumed for illumination. Subsequently, we find that states with identical initial discord can lead to varying advantages, indicating that the usable portion of discord for illumination depends on additional structural features of the state. Then, we consider the relation between the advantage and both entanglement and discord by performing a conditional extremal analysis. To this end, for states clustered by identical advantage and initial discord, we compute the maximum and minimum initial entanglement within each cluster. We demonstrate that, for states with fixed initial discord, the maximum (and not minimum) entanglement increases by increment of the advantage. We conclude that for any given initial discord, higher entanglement is a sufficient (but not necessary) resource for higher advantage. On the other hand, for states clustered by identical advantage and initial entanglement, we compute the maximum and minimum initial discord in each group. Here, the minimum (and not always maximum) discord scales monotonically with advantage. It shows that, for fixed initial entanglement, higher discord is a necessary (but not always sufficient) resource for higher advantage. This result provides a refined, operational perspective on how different forms of quantum correlations govern the performance of the illumination protocol. We finally find a persistent linear dependence of the advantage on initial discord in the high-noise regime, highlighting discord as the key resource for resilience to noise in the protocol.