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arXiv:2602.09468 · Quantum Information Processing

Resources of the advantage in quantum illumination: Discord and entanglement

Mojtaba Asadollahi, Mohammad Hossein Zarei

quant-phSubmitted Feb 10, 2026• Announced Feb 11, 2026• 0 citations• Revised Oct 6, 2026 (v3)

v1 · Feb 10, 2026 v2 · Jun 30, 2026 v3 · Oct 6, 2026

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, high entanglement restricts the accessible advantage to high values, making high entanglement sufficient for high advantage. Conversely, at fixed entanglement, low discord limits the advantage to low values, indicating that high discord is necessary for high advantage. 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.

Comments: 14 pages, 9 figures, accepted for publication in Quantum Information Processing

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We cast the problem of illuminating an object in a noisy environment into a communication protocol. A probe is sent into the environment, and the presence or absence of the object constitutes a signal encoded on the probe. The probe is then measured to decode the signal. We calculate the Holevo information and bounds to the accessible information between the encoded and received signal with two different Gaussian probes---an Einstein-Podolsky-Rosen (EPR) state and a coherent state. We also evaluate the Gaussian discord consumed during the encoding process with the EPR probe. We find that the Holevo quantum advantage, defined as the difference between the Holevo information obtained from the EPR and coherent state probes, is approximately equal to the discord consumed. These quantities become exact in the typical illumination regime of low object reflectivity and low probe energy. Hence we show that discord is the resource responsible for the quantum advantage in Gaussian quantum illumination.

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Measurements of Quantum Systems disturb their states. To quantify this non-classical characteristic, Zurek and Ollivier introduced the quantum discord, a quantum correlation which can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers exponential speed up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy, and identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.

Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we experimentally demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this ‘quantum advantage’.

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