Lakshmanan, Theerthagiri (2024) Target detection with quantum illumination and entanglement generation through heisemberg exchange interaction. [Tesi di dottorato]

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Abstract

In cases where entanglement is disrupted, quantum illumination (QI) surpasses classical illumination significantly in target detection. The superiority of QI was previously measured using a Bayesian framework, assuming equal likelihood of the target's presence or absence, with error probability as the performance metric. However, radar theory favors the Neyman-Pearson performance criterion over the Bayesian approach. The Neyman-Pearson criterion sidesteps challenges related to assigning appropriate prior probabilities to target presence and absence, as well as the associated costs of false alarms and missed detections. This study utilizes findings from our phase conjugate receiver (PC) and Correlation-To-Displacement (C-D) receiver research to compute the receiver operating characteristic, which illustrates the trade-off between detection probability and false alarm probability. This analysis aims to optimize QI target detection under the Neyman-Pearson criterion. The correlation-To-Displacement (C-D) receiver is studied in this thesis first part. Entanglement is vulnerable to degradation in a noisy sensing scenario, but surprisingly, the quantum illumination protocol has demonstrated that its advantage can survive. However, designing a measurement system that realizes this advantage is challenging since the information is hidden in the weak correlation embedded in the noise at the receiver side. Recent progress in a correlation-to-displacement conversion module provides a route towards an optimal protocol for practical microwave quantum illumination. In this work, we extend the conversion module to accommodate experimental imperfections that are ubiquitous in microwave systems. To mitigate loss, we propose amplification of the return signals. In the case of ideal amplification, the entire six-decibel error-exponent advantage in target detection error can be maintained. However, in the case of noisy amplification, this advantage is reduced to three-decibel. We analyze the quantum advantage under different scenarios with a Kennedy receiver in the final measurement. In the ideal case, the performance still achieves the optimal one over a fairly large range with only on-off detection. Empowered by photon number resolving detectors, the performance is further improved and also analyzed in terms of receiver operating characteristic curves. Our findings pave the way for the development of practical microwave quantum illumination systems. In the second part of this thesis, we generate the $W$ entangled state through Heisenberg exchange interaction. The spread of entanglement is a problem of great interest. It is particularly relevant to quantum state synthesis, where an initial direct-product state is sought to be converted into a highly entangled target state. In devices based on pairwise exchange interactions, such a process can be carried out and optimized in various ways. As a benchmark problem, we consider the task of spreading one excitation among $N$ two-level atoms or qubits which is the typical feature of a $W$ state. Starting from an initial state where one qubit is excited, we seek a target state where all qubits have the same excitation amplitude a generalized-$W$ state. This target is to be reached by suitably chosen pairwise exchange interactions. For example, we may have a a setup where any pair of qubits can be brought into proximity for a controllable period of time. We describe three protocols that accomplish this task, each with $N-1$ tightly-constrained steps. In the first, one atom acts as a flying qubit that sequentially interacts with all others. In the second, qubits interact pairwise in sequential order. In these two cases, the required interaction times follow a pattern with an elegant geometric interpretation. They correspond to angles within the spiral of Theodorus -- a construction known for more than two millennia. The third protocol follows a divide-and-conquer approach -- dividing equally between two qubits at each step. For large $N$, the flying-qubit protocol yields a total interaction time that scales as $\sqrt{N}$, while the sequential approach scales linearly with $ N$. For the divide-and-conquer approach, the time has a lower bound that scales as $\ln N$. With any such protocol, we show that the phase differences in the final state cannot be independently controlled. For instance, a W-state (where all phases are equal) cannot be generated by pairwise exchange.

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