(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

We propose a structured receiver for optimum mixed-state discrimination in quantum illumination target detection, paving the way for entanglement-enhanced minimum-error-probability sensing in an entanglement-breaking environment.

/pdf/optimum-mixed-state-discrimination-for-noisy-entanglement-14m4nzj096.pdf

Optimum mixed-state discrimination for noisy entanglement-enhanced sensing

Lossy bosonic channels play an important role in a number of quantum information tasks, since they well approximate thermal dissipation in an experiment. Here, we characterize their metrological power in the idler-free and entanglement-assisted cases, using respectively single- and two-mode Gaussian states as probes. In the problem of estimating the loss parameter, we study the power-constrained quantum Fisher information (QFI) for generic temperature and loss parameter regimes, showing qualitative behaviours of the optimal probes. We show semi-analytically that the two-mode squeezed-vacuum state optimizes the QFI for any value of the loss parameter and temperature. We discuss the optimization of the total QFI, where the number of probes is allowed to vary by keeping the total power constrained. In this context, we elucidate the role of the ‘shadow-effect’, or passive signature, for reaching a quantum advantage. Finally, we discuss the implications of our results for the quantum illumination and quantum reading protocols.

https://iopscience.iop.org/article/10.1088/1751-8121/ac83fa/pdf

Gaussian quantum estimation of the loss parameter in a thermal environment

While quantum entanglement can enhance the performance of several technologies such as computing, sensing and cryptography, its widespread use is hindered by its sensitivity to noise and losses. Interestingly, even when entanglement has been destroyed, some tasks still exhibit a quantum advantage $Q$, defined by a $Q$-time speedup, over any classical strategies. A prominent example is the quantum radar, which enhances the detection of the presence of a target in noisy surroundings. To beat all classical strategies, Lloyd proposed to use a probe initially entangled with an idler that can be recombined and measured with the reflected probe. Observing any quantum advantage requires exploiting the quantum correlations between the probe and the idler. It involves their joint measurement or at least adapting the idler detection to the outcome of the probe measurement. In addition to successful demonstrations of such quantum illumination protocols at optical frequencies, the proposal of a microwave radar, closer to conventional radars, gathered a lot of interest. However, previous microwave implementations have not demonstrated any quantum advantage as probe and idler were always measured independently. In this work, we implement a joint measurement using a superconducting circuit and demonstrate a quantum advantage $Q>1$ for microwave radar. Storing the idler mitigates the detrimental impact of microwave loss on the quantum advantage, and the purity of the initial entangled state emerges as the next limit. While the experiment is a proof-of-principle performed inside a dilution refrigerator, it exhibits some of the inherent difficulties in implementing quantum radars such as the limited range of parameters where a quantum advantage can be observed or the requirement for very low probe and idler temperatures. 

/pdf/quantum-advantage-in-microwave-quantum-radar-2q7cn89a.pdf

Quantum advantage in microwave quantum radar

Quantum radars and lidars are a novel, much-discussed, and rapidly evolving field of quantum science and technology, promising remarkable advantages in such basic tasks as target detection, ranging, and recognition. Quantum radars and lidars have already moved from the realm of theoretical considerations toward experiments, green, and as is the case for lidars, toward practical applications. Here we review the underlying concepts and present the basic configurations of quantum radars and lidars based on photonic entanglement and single-photon detection. We also briefly discuss the methods of producing entangled photons, such as spontaneous parametric down conversion (SPDC), spontaneous four-wave mixing, Josephson parametric amplifiers (JPAs), and quantum antennas. We show that quantum technologies open promising avenues toward the enhancement of signal-to-noise ratio (SNR) and overcoming the Rayleigh limit in radar and lidar systems. 

/pdf/quantum-radars-and-lidars-concepts-realizations-and-1cs72o4x.pdf

Quantum Radars and Lidars: Concepts, realizations, and perspectives

We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons N S transmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of √2 in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is ln(1 + 1/N S ) larger than the optimal classical setup, in the N S « 1 regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.

/pdf/a-comparison-between-quantum-and-classical-noise-radar-4w953qmti7.pdf

A comparison between quantum and classical noise radar sources

An adaptive revisit interval selection (RIS) in multifunction radars is an integral part of efficient time budget management (TBM). In this paper, the RIS problem is formulated as a Markov decision process (MDP) with unknown state transition probabilities and reward distributions. A reward function is proposed to minimize the tracking load (TL) while maintaining the track loss probability (TLP) at a tolerable level. The reinforcement learning (RL) problem is solved using the Q-learning algorithm with an epsilon-greedy policy. Compared to a baseline algorithm, the RL approach was capable of maintaining the tracks while reducing the tracking load significantly.

/pdf/time-budget-management-in-multifunction-radars-using-2oxbbpx8s1.pdf

Time Budget Management in Multifunction Radars Using Reinforcement Learning

We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons $N_S$ transmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of $\sqrt{2}$ in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is $\ln(1+1/N_S)$ larger than the optimal classical setup, in the $N_S\ll1$ regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.

/pdf/a-comparison-between-quantum-and-classical-noise-radar-4e27axmh3u.pdf

Anders Strom

Papers

A comparison between quantum and classical noise radar sources

Time Budget Management in Multifunction Radars Using Reinforcement Learning

A comparison between quantum and classical noise radar sources