Resources of the advantage in quantum illumination: Discord and entanglement

Abstract

We investigate how the quantum advantage in quantum illumination is determined by an interplay between entanglement and discord of the probe state. In particular, we consider a setup in which the probe is a maximally mixed marginal (MMM) state and the environmental state is completely mixed where the quantum advantage equals the amount of discord consumed for illumination. Through a conditional extremal analysis, we determine the range of accessible advantages for given values of entanglement and discord. At fixed discord, higher entanglement restricts the accessible advantage to higher values, making high entanglement sufficient for achieving high advantage. Conversely, at fixed entanglement, low discord limits the advantage to low values, indicating that high discord is necessary for high advantage in MMM states. These conclusions remain unchanged when alternative correlation measures, including relative entropy and Bures entanglement and geometric discord, are used. The consistency of our results across multiple conceptually distinct measures indicates that the observed resource-advantage relation is not an artifact of a specific quantifier, but a robust feature of the protocol within the family of MMM states. We finally find that in the high-noise regime (near-maximally-mixed state), quantum advantage is, to leading order, a linear function of the initial discord highlighting discord as the key resource for resilience to noise in the protocol.