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arXiv:2511.05125

Channel Superposition Mitigates Photon Loss Errors in Quantum Illumination

Fei Li, Xiao-Wei Li, Oscar Dahlsten

quant-phSubmitted Nov 7, 2025• Announced Nov 10, 2025• 0 citations
arXivHTMLPDF

Abstract

In quantum illumination, the probe photon is entangled with an ancilla photon, and both are jointly measured at the end. The entanglement between the probe and ancilla photons enhances the detection performance per unit average photon number in the probe mode, particularly in low-reflectivity and high-noise scenarios. However, photon loss severely limits the practical advantage of such protocols. To address this, we employ a channel superposition framework, which encompasses two kinds of channel superposition protocols: indefinite causal order (ICO) and path superposition with disjoint environment (PS-DE). Our analytical and numerical analysis based on the quantum Chernoff bound shows that both ICO and PS-DE can, in principle, achieve an advantage. The advantage persists as long as non-zero interference remains, reverting to the performance of standard quantum illumination once the interference is completely suppressed. Crucially, the ICO protocol is significantly more robust, maintaining a tighter upper bound on the error probability than standard quantum illumination and the PS-DE approach. This performance hierarchy is rooted in their fundamental structures: ICO exploits a shared environment to generate stronger quantum interference, while PS-DE, relying on disjoint environments, offers a more experimentally tractable albeit less potent alternative.

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In quantum illumination, the probe photon is entangled with an ancilla photon, and both are jointly measured at the end. The entanglement between the probe and ancilla photons enhances the detection performance per unit average photon number in the probe mode, particularly in low-reflectivity and high-noise scenarios. However, photon loss severely limits the practical advantage of such protocols. To address this, we employ a channel superposition framework, which encompasses two kinds of channel superposition protocols: indefinite causal order (ICO) and path superposition with disjoint environment (PS-DE). Our analytical and numerical analysis based on the quantum Chernoff bound shows that both ICO and PS-DE can, in principle, achieve an advantage. The advantage persists as long as non-zero interference remains, reverting to the performance of standard quantum illumination once the interference is completely suppressed. Crucially, the ICO protocol is significantly more robust, maintaining a tighter upper bound on the error probability than standard quantum illumination and the PS-DE approach. This performance hierarchy is rooted in their fundamental structures: ICO exploits a shared environment to generate stronger quantum interference, while PS-DE, relying on disjoint environments, offers a more experimentally tractable albeit less potent alternative.
In quantum illumination, the probe and idler photons are entangled, and both are jointly measured at the end. The entanglement between the probe and idler photons enhances the detection performance per unit average photon number in the probe mode, particularly in low-reflectivity and high-noise scenarios. However, photon loss degrades the absolute detection performance and progressively reduces the performance gain relative to optimal classical strategies by diminishing non-classical correlations. To address this, we employ a channel superposition framework that encompasses two types of channel superposition protocols: indefinite causal order (ICO) and path superposition with a disjoint environment (PS-DE). Under the effective erasure/fading loss model adopted for the low-brightness regime, our analytical and numerical analysis based on the quantum Chernoff bound shows that both ICO and PS-DE can, in principle, achieve an advantage. The advantage persists as long as non-zero interference remains, reverting to the performance of standard quantum illumination once the interference is completely suppressed. Crucially, within this model, the ICO protocol is significantly more robust, maintaining a tighter upper bound on the error probability than standard quantum illumination and the PS-DE approach. This performance hierarchy is rooted in their fundamental structures: ICO exploits a shared environment to generate stronger quantum interference, while PS-DE, relying on disjoint environments, offers a more experimentally tractable, albeit weaker, alternative.
Quantum illumination can be used to detect the low-reflectivity target hidden in strong background noise. All known results are based on the assumption of ideal photon transmission and reception. In this paper, we investigate the impact of photon loss on the performance of quantum illumination in two distinct scenarios: (I) the probabilistic loss mode and (II) the hybrid loss model. In both scenarios it is shown that quantum illumination with bipartite entanglement outperforms its classic correspondence with coherent states in both error probability and its response to probabilistic photon loss. Moreover, in scenario I, the resource required in quantum illumination scales far less than 1/pch21/{p}_{\mathrm{ch}}^{2}1/pch2​ to completely compensate the channel efficiency pch2{p}_{\mathrm{ch}}^{2}pch2​. This poses a sharp contrast with the consumption of classic illumination which scales as $\ensuremath{\gg}1/{p}_{\mathrm{ch}}^{2}$. However in scenario II, both quantum illumination and classic illumination need resources of more than 1/pch21/{p}_{\mathrm{ch}}^{2}1/pch2​, due to extra thermal noise introduced in the hybrid loss model.
Quantum illumination is one of the most basic ways to realize the quantum radar for detection of low-reflectivity targets embedded in a thermal-noise bath. It preserves a strong advantage over the classical counterparts even though its fragile quantum entanglement is completely destroyed by a large amount of noise and losses. In this paper, we describe and analyze a discrete-variable quantum illumination system with ancillary degrees of freedom of entangled photon pairs. Comparing the error probability bound, i.e., the quantum Chernoff bound, we identify that this system indeed offers higher accuracy than the single-photon illumination and quantum illumination with single degree of freedom of entangled photon pairs. Furthermore, the utilization of ancillary degrees of freedom exponentially enhances signal-to-noise ratio over quantum illumination without ancillary degrees of freedom. It means that this system reduces the necessary amount of signal photons to accurately determine whether the object is present or absent in the target region, which is absolutely crucial to the stealthiness of the radar system.
Abstract Quantum illumination is an emerging quantum technology that can detect whether a weakly reflecting target is present or absent in highly noisy environments. For practical purposes, in this paper we analyze the performance limit of a quantum illumination scheme and that of a classical illumination scheme in the presence of photon loss. The performance advantage of quantum illumination over classical illumination is addressed in settings of symmetric and asymmetric hypothesis testings. We analyze the effects of photon loss and discuss the relevant physical mechanisms. In addition, we demonstrate that noiseless linear amplification can be used to enhance the performance advantage. Our results are a foray into confirmation of the validity of quantum illumination and show more realistic performance advantage for practical applications.
Indefinite causal ordering (ICO) refers to quantum channels arranged so that the path through them is a super- position of different possible paths. The ICO is called pure when the path superposition is a pure quantum state. Channel probing, in which probes in prepared quantum states are passed through copies of the channel to estimate one or more channel parameters, is aided by ICO. Specifically, pure ICO is known to increase the quantum Fisher information (QFI) in the processed probe state about the unknown parameter(s). We consider the case complementary to pure ICO in which the path state is maximally mixed for a given indefiniteness. Deriving the QFI under this condition by a new approach, we find that mixed ICO-assisted probing, while not as beneficial as pure ICO probing, still yields greater QFI than does the comparable scheme with definite causal order. The d-dimensional quantum depolarizing channel is used as the channel model for this study. While mixed ICO-assisted probing, like pure ICO-assisted probing, is generally advantageous for probing the depolarizing channel, mixed ICO's relative effectiveness decreases with probe dimension, just as for pure ICO-assisted probing, each being most effective for qubit probes.
Quantum illumination takes advantage of quantum entanglement to achieve low error probability for detecting a low reflective object embedded in a noisy thermal bath. The two-mode squeezed state (TMSS), which is a Gaussian state, has been applied to quantum illumination as the detecting states in experiment. The photon-subtracted TMSS has also been proposed to achieve even lower error probability. Here we study quantum illumination with non-Gaussian states generated by photon subtraction and photon addition. Helstrom limit and quantum Chernoff bound are evaluated for comparison between performance of states with the same squeezing strength and with the same signal strength, respectively. Particularly, states generated by asymmetrical coherent superposition of photon subtraction and addition are studied, which are shown by us to have better performance than symmetrical ones. We show that non-Gaussian operations enhance the quantum illumination by introducing both stronger entanglement and signal strength. We then give a strategy on how to choose the optimal states for the best performance in different scenarios.