The ability to determine distances from dedicated measurements, namely active ranging, is crucial in a variety of systems including localization, radar, and lidar. This thesis establishes the quantum limits and determines the quantum advantage provided by single-beam displaced squeezed states in active ranging. Analytical expressions of the quantum Fisher information (QFI) are provided for monochromatic and continuous-mode waves passing through a thermal loss channel with arbitrary loss and noise conditions. The optimal allocation of system resources for performing displacement and squeezing operations is determined. The optimal allocation consists of apportioning all resources to perform either the displacement operation, providing no quantum advantage, or the squeezing operation. Analytical results are examined in optical and microwave regimes. The optimal gain, i.e., the ratio between the QFI obtained by optimal resource allocation and the QFI obtained by performing only the displacement operation, is derived for the optical and microwave regimes. Quantum advantage afforded by the prototypical heterodyne receiver is also investigated. The results of this thesis pave the way for establishing a foundation of active ranging and provide insights for system design employing currently available quantum technologies.
The ability to determine distances from dedicated measurements, namely active ranging, is crucial in a variety of systems including localization, radar, and lidar. This thesis establishes the quantum limits and determines the quantum advantage provided by single-beam displaced squeezed states in active ranging. Analytical expressions of the quantum Fisher information (QFI) are provided for monochromatic and continuous-mode waves passing through a thermal loss channel with arbitrary loss and noise conditions. The optimal allocation of system resources for performing displacement and squeezing operations is determined. The optimal allocation consists of apportioning all resources to perform either the displacement operation, providing no quantum advantage, or the squeezing operation. Analytical results are examined in optical and microwave regimes. The optimal gain, i.e., the ratio between the QFI obtained by optimal resource allocation and the QFI obtained by performing only the displacement operation, is derived for the optical and microwave regimes. Quantum advantage afforded by the prototypical heterodyne receiver is also investigated. The results of this thesis pave the way for establishing a foundation of active ranging and provide insights for system design employing currently available quantum technologies.
Quantum ranging is crucial in several applications such as radar and localization. This paper determines the quantum advantage of ranging with single-mode displaced squeezed states. Exact analytical expressions for the quantum Fisher information (QFI) about the range parameter are derived in the presence of thermal loss channels characterized by arbitrary loss and noise parameters. The quantum advantage, termed as gain, is determined as a ratio of QFI with and without employing squeezing. It is shown that the gain can be unboundedly large in the optical regime whereas it is upper bounded in the microwave regime.
Quantum light promises improved precision in optical remote sensing, but its practical advantage depends critically on whether nonclassical resources remain useful under realistic noise and experimentally accessible detection. This question becomes especially relevant for LiDAR systems, where a quantum advantage has been demonstrated for target detection and joint range-velocity estimation, but mostly under idealized conditions or simple noise models, such as optical loss and thermal background. A key open point is whether entanglement provides an operational advantage when the dominant disturbance is not independent noise, but structured interference across sensing modes. Here, we address this question by studying the joint estimation of target range and velocity with bright two-mode Gaussian probes and homodyne detection, comparing coherent, separable squeezed, and twin-beam states at a fixed resource budget. Our results reveal a hierarchy of quantum resources set by the noise structure: separable squeezing provides a robust advantage over coherent illumination under loss and thermal background, whereas twin-beam probes become superior under correlated jamming when the receiver is adaptively optimized. These results establish correlated noise as the operational regime in which entanglement provides a robustness advantage beyond local squeezing, opening a receiver-aware route to quantum-enhanced LiDAR in realistic and potentially adversarial environments.
Abstract Quantum Fisher information quantifies the sensitivity encoded in a parameter-dependent quantum state, whereas the performance of a practical sensor is limited by the information that survives the physical channel and can be extracted by the available receiver. We introduce an accessible Fisher-information framework based on a physically admissible family of measurements and use it to separate state-level sensitivity, channel degradation, and receiver limitations. The framework is applied to Ramsey and NOON interferometry, squeezed-state displacement sensing, two-level thermometry, and multiparameter qubit sensing. We show that resource normalization, finite visibility, readout errors, measurement rank, shot allocation, calibration uncertainty, and nuisance parameters can substantially modify the experimentally available advantage. For squeezed-state sensing, homodyne-axis misalignment produces a finite optimal squeezing, while bounded calibration uncertainty leads to a robust operating rule. In the pure-loss model considered here, attenuation reduces the attainable information without shifting this optimum. The results provide practical design rules that connect quantum-enhanced state preparation with realistic measurement constraints and experimentally extractable sensing performance.
This thesis presents three studies in quantum-enhanced sensing and target detection. The first study explores covert target detection using optical or microwave probes, establishing quantum-mechanical limits on the error probabilities of entanglement-assisted detection methods while maintaining the sender's covertness. It identifies the minimal energy required to preserve covertness and reduce error probabilities, compares two-mode squeezed vacuum probes and coherent states against these limits, and extends the analysis to discriminating thermal loss channels and non-adversarial quantum illumination. The second study focuses on phase-insensitive optical amplifiers, determining the quantum limit on the precision of gain estimation using multimode probes possibly entangled with ancillary systems. It finds that the average photon number and the number of input modes are interchangeable resources for achieving optimal gain sensing precision, contrasting classical probes with quantum probes and highlighting the advantages of the latter, even with single-photon inputs and inefficient photodetection. It also provides a closed-form expression for the energy-constrained Bures distance between two amplifier channels. The third study compares three probe states -- coherent state, two-mode squeezed vacuum (TMSV), and single-photon entangled state (SPES) -- in quantum-enhanced target detection, assessing their performance under signal energy constraints relevant to covert radar sensing. SPES is uniquely positioned as a practical probe due to its non-classical properties after thermal loss and ease of generation. Numerical analysis shows that at low signal energies, the error exponent of TMSV aligns with SPES, indicating comparable detection capabilities and that SPES surpasses the best classical state-the coherent state-in accuracy for certain signal strengths.
An important problem in quantum information theory is finding the best possible performance of the optical communication channel employing suitable codewords, receiver design, and constellation optimization techniques. Many receiver designs have been studied in the past to discriminate Phase-Shift Keying (PSK) quantum states that are used to encode information before transmitting over the communication channel. Among many types of quantum states, there has been significant work on the use of coherent states for encoding information. Previous work has sought to improve the communication performance in terms of various metrics such as error probability of state discrimination and capacities by employing a number of quantum states such as coherent states and squeezed-displaced states. In this thesis, we provide optimal receiver design employing coherent states and squeezed-displaced states to maximize the mutual information and lower the error probability of state discrimination. In the case of pure coherent states, we derive an alternative channel capacity of phase-shift keying coherent state with a realizable displacement receiver by maximizing mutual information over symbol priors and pre-detection displacement. We find that the capacity is higher than the capacity achieved by maximizing mutual information over symbol prior but with zero displacements. The overall scheme demonstrates designing an improved, yet easy-to-implement receiver for better communication performance by tuning it at different photon number regime. We also explore the use of squeezing operations with a displacement receiver for state discrimination. Our calculation demonstrates that we see no performance improvement in terms of the probability of error of state discrimination or mutual information using displacement receivers when optimal squeezing on the transmitter side is used. In addition, we also study the receiver design scheme for QPSK modulation where squeezing is employed at the receiver side. We find that using the squeezing operation on the receiver side provides an advantage in terms of increased mutual information for the low-photon number regime compared to when no squeezing is used. In the later part of the thesis, we study entanglement-assisted communication using two-mode squeezing vacuum. The use of pre-shared entanglement in entanglement-assisted communication provides a superior alternative to classical communication specifically in the low brightness regime and highly noisy environment. In this thesis, we analyze the performance of a few low-complexity receivers that employ optical parametric amplifiers. In the simulation, we demonstrate that receiver designs with an entanglement-assisted scheme using phase-shift-keying modulation can outperform classical capacities. We describe a newly proposed 2x2 optical hybrid receiver for entanglement-assisted communication whose performance is roughly 10% better in terms of error probability as compared to previously proposed optical parametric amplifier-based receivers. Further, we find that using unequal priors for BPSK provides approximately three times the advantage over equal priors in terms of information rate.
In this thesis we make progress towards applications of quantum estimation theory to new physical systems. We first consider two commonly visited problems in quantum metrology: source optimisation and source localisation. For the first, we focus on estimating the distances, d, between neighbouring light sources along an array, which undergoes stretching deformations. We evaluate how changing the nature of the sources impacts the estimation precision of d by using the quantum Fisher information (QFI) as a figure of merit. By comparing this quantity for arrays of single photon emitters, coherent, thermal, and entangled sources, we find that the classical coherent and thermal states outperform the single photon emitters. This would be favourable since generating classical states is less resource-expensive to create. However, a quantum enhancement is observed when entanglement is employed. In agreement with separate work, the optimal state is that which entangles the eigenstates corresponding to the maximum and minimum difference eigenvalues of the generator. We demonstrate that not all entangled states can reproduce similar precision enhancements. This insight is reminiscent of previous studies, where entanglement was concluded as a necessary but insufficient resource for quantum metrology.
Next, we address the source localisation problem to detect any deformations applied to a grid of sources. Improving this detection depends on our ability to engineer grids that maximise the sensitivity of the QFI matrix. Hence, we derive the generators of local translations of unitary evolutions that describe any general grid deformation, and show that our result is a multi-parameter extension of other results in the literature. We obtain a general result for the quantum Fisher information matrix (QFIM) through these generators for any grid deformation and explore specific spatial maps, including composite stretches, shears, and rotations. Since the QFI matrix depends only on the properties of the probe state and the configuration of the emitters, we explore how we can modify both to enhance our estimation sensitivity to determine the applied grid deformation. Physically motivated, we find the best arrangement of sources that enhances the sensitivity of detection for a set number of sources.
Finally, we consider the optimal estimation of a complex squeezing operation in phase space. The use of squeezed light as a quantum resource is ubiquitous in quantum optics, and a complete characterisation of a complex squeezing operation is pivotal for fundamental reasons. This is a true multi-parameter quantum estimation problem of incompatible observables. Specifically, we find that the symmetric logarithmic derivates (SLDs) for amplitude and directional squeezing do not commute. This prohibits simultaneous optimal estimates of both parameters, even in the asymptotic limit. As a result, we focus on finding separable optimal estimates. The Cramer-Rao bound is determined to provide a theoretical benchmark on the bi-variate estimation precision for general single mode Gaussian probes. Using this and the SLDs, we present a practical experimental implementation that can realise the individual fundamental precision bounds.