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We propose optimal observables for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes the discrimination error between the presence and absence of a low-reflectivity target using Gaussian states. The optimal observables dominantly consist of off-diagonal components of output states, which is implemented with feasible setups. In the quantum regime using a two-mode squeezed vacuum state, the receiver implemented with heterodyne detections outperforms the other feasible receivers, which asymptotically improves the error probability exponent by a factor of two over the classical state bound. In the classical regime using coherent or thermal states, the receiver implemented with photon number difference measurement asymptotically approaches its bound.
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Quantum illumination is the task of determining the presence of an object in a noisy environment. We determine the optimal continuous variable states for quantum illumination in the limit of zero object reflectivity. We prove that the optimal single mode state is a coherent state, while the optimal two mode state is the two-mode squeezed-vacuum state. We find that these probes are not optimal at non-zero reflectivity, but remain near optimal. This demonstrates the viability of the continuous variable platform for an experimentally accessible, near optimal quantum illumination implementation.
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.
With the aim to loosen the entanglement requirements of quantum illumination, we study the performance of a family of Gaussian states at the transmitter, combined with an optimal and joint quantum measurement at the receiver. We find that maximal entanglement is not strictly necessary to achieve quantum advantage over the classical benchmark of a coherent-state transmitter, in both settings of symmetric and asymmetric hypothesis testing. While performing this quantum-classical comparison, we also investigate a suitable regime of parameters for potential short-range radar (or scanner) applications.
The quantum illumination is examined by making use of the three-mode maximally entangled Gaussian state, which involves one signal and two idler beams. It is shown that the quantum Bhattacharyya bound between $rho$ (state for target absence) and $sigma$ (state for target presence) is less than the previous result derived by two-mode Gaussian state when $N_S$, average photon number per signal, is less than $0.295$. This indicates that the quantum illumination with three-mode Gaussian state gives less error probability compared to that with two-mode Gaussian state when $N_S < 0.295$.
Heisenbergs uncertainty relations for measurement quantify how well we can jointly measure two complementary observables and have attracted much experimental and theoretical attention recently. Here we provide an exact tradeoff between the worst-case errors in measuring jointly two observables of a qubit, i.e., all the allowed and forbidden pairs of errors, especially asymmetric ones, are exactly pinpointed. For each pair of optimal errors we provide an optimal joint measurement that is realizable without introducing any ancilla and entanglement. Possible experimental implementations are discussed and Toronto experiment [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] can be readily adapted to an optimal joint measurement of two orthogonal observables.
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