Quantum states are ultimately responsible for numerous counterintuitive phenomena that defy classical intuition. As the development of quantum technologies accelerates, our ability to harness these quantum resources becomes essential. This review addresses a fundamental question. How do we quantify the quantumness of a state, and which specific traits distinguish it from its classical counterparts? We examine quantumness through both theoretical and operational lenses, providing a clear framework for state characterization. Ultimately, we demonstrate that certifying quantumness is not just a theoretical exercise. It is a practical necessity for identifying, and realizing quantum advantage in real-world applications.
Quantum states are ultimately responsible for numerous counterintuitive phenomena that defy classical intuition. As the development of quantum technologies accelerates, our ability to harness these quantum resources becomes essential. This review addresses a fundamental question. How do we quantify the quantumness of a state, and which specific traits distinguish it from its classical counterparts? We examine quantumness through both theoretical and operational lenses, providing a clear framework for state characterization. Ultimately, we demonstrate that certifying quantumness is not just a theoretical exercise. It is a practical necessity for identifying, and realizing quantum advantage in real-world applications.
Quantum states and measurements are two central physical objects in the theory of quantum mechanics. The preparation, control and measurement of quantum states lies at the heart of modern quantum information processing protocols ranging from secure communication to quantum computation and precision sensing. And yet, the reliable operation of these advanced protocols ultimately rests on a far more essential prerequisite - our ability to calibrate, certify and benchmark the quantum states we prepare and the quantum measurements we perform. Quantum information theory provides a natural framework for these tasks, meaningfully connecting the resources we expend for characterisation with the accuracy and precision we can expect in return. While decades of advances in quantum information have refined our understanding of quantum characterisation and sharpened our practical ability to calibrate with enhanced precision, important questions about the fundamental limits of quantum characterisation remain unanswered. Although incorporating entanglement at the measurement stage is known to enhance the estimation of unknown quantum states, the extent of this improvement remains poorly understood. This leaves open a fundamental question on the utility of complex entangling measurement strategies, impeding progress towards bridging the significant gap between practically achievable precision and the ultimate theoretical quantum limit. Complementary to quantum state estimation, which is relatively well-established in theory and practice, the characterisation of quantum measurements lacks a rigorous information-theoretic foundation, leading to a dearth of principled benchmarks and provably optimal strategies despite growing experimental interest. This thesis develops and applies information-theoretic tools to answer questions in quantum characterisation, with an eye to enabling practical improvements beyond current techniques in the field. First, we introduce a computable measure of entanglement enhancement for quantum state estimation and study its variation across general multi-parameter estimation problems for higher-dimensional quantum states. We show that the entanglement enhancement is maximised for full qudit state tomography but grows only linearly with system dimension even when allowing an asymptotically large number of entangling operations. Our proposed tight upper bound to entanglement enhancement therefore constitutes a strong limitation on the utility of such entangling measurements. Next, we formulate the dual problem of quantum detector estimation, developing a comprehensive framework for maximally precise calibration centred around a newly introduced quantity - the detector quantum Fisher information. This information-theoretic measure stipulates the ultimate precision attainable for measurement calibration and identifies the optimal input states that achieve this precision. Further, our framework enables the first provably optimal detector estimation experiment and reveals the scope for entanglement-based enhancements, thereby placing measurement characterisation on equal footing with state characterisation. Considered together, these results suggest two contrasting conclusions about quantum characterisation. On the one hand, they show that for quantum state estimation, increasingly powerful entangling measurements offer only diminishing returns at the ultimate precision limit. On the other hand, they highlight practical quantum advantages available for detector estimation by providing a framework that can improve calibration performance and guide future experimental design. More broadly, these results complete and advance the triad of state, process, and detector characterisation, positioning quantum information measures as not merely abstract bounds, but practical guides for deciding when complex quantum resources are genuinely worth deploying and where near-term quantum advantages are most likely to be realised.
Quantum technologies in the areas of metrology, cryptography and computation, both theoretical and practical, are exceeding the limits that are classically possible, and even approaching the ultimate quantum limits. Despite rapid advances, experimental implementation of these technologies remains limited to small systems. The key question of this thesis is whether, through the use of alternate resources, quantum technologies can be brought closer to experimental feasibility. We investigate two application areas: quantum tomography, the experimental characterization of a quantum state or processes and quantum clock synchronization. Quantum tomography is fundamental to all quantum technologies, yet experimentalists have prepared quantum states that surpass existing characterization techniques. A key result of this dissertation is that popular experimental techniques can be improved through an alternative choice of measurement settings based on the geometry of Platonic solids. The change requires no increased complexity in the experimental apparatus. We also derive a novel numerical technique for reconstructing quantum states and processes from measured data. We frame the problem as a semidefinite program, an optimization problem that may be solved efficiently. We also develop a novel adaptive tomography technique, in which the time spent on each measurement adapts based on previous measurement outcomes. Finally to understand the average performance of different tomography schemes we need a notion of a prior distribution over quantum states. We derive a new prior over quantum states based on a recently derived state distinguishability measure, the quantum Chernoff bound. The best classical algorithms to synchronize clocks achieve the so called standard quantum limit. Quantum clock synchronization protocols have already surpassed this limit and theoretical proposals even reach the ultimate Heisenberg limit. However, these protocols rely on a resource known as entanglement, limiting their current feasibility. We develop a novel quantum clock synchronization protocol with performance close to the Heisenberg limit yet requiring no entanglement. We also develop an optical proof of principle realization of the clock synchronization scheme that requires only existing experimental apparatus.
Quantum optics is the branch of physics that investigates the interaction of light with matter at the quantum level, where the discrete nature of photons and quantum states of atoms, molecules, and solid-state systems become dominant. Quantum optics systems provide the experimental and theoretical foundation for understanding nonclassical states of light, quantum coherence, entanglement, and measurement at the quantum limit. Over the past few decades, advances in laser technology, nonlinear optics, and precision measurement have transformed quantum optics from a fundamental discipline into a key enabler of quantum technologies, including quantum communication, quantum computing, quantum sensing, and quantum metrology. This review presents a comprehensive overview of the physical principles, system architectures, and experimental platforms of quantum optics. Emphasis is placed on light sources, atom–photon interaction systems, detection techniques, and emerging applications, along with current challenges and future research directions.
As a cornerstone of quantum science and technology, quantum precision measurement aims to transcend the standard quantum limit (SQL) and achieve sensitivities unattainable by classical approaches by harnessing distinctive quantum resources such as entanglement, squeezing and non-Gaussianity. Within this framework, Gaussian states have historically played a central role, underpinning a series of seminal experimental advances; however, their utility in metrology is fundamentally bounded by theoretical constraints that preclude unlimited gains in measurement precision. In contrast, a growing body of recent research has revealed that non-Gaussian states–endowed with stronger quantum correlations and more pronounced non-classical characteristics — can significantly surpass Gaussian counterparts in key tasks such as phase estimation, quantum imaging and quantum sensing. Under specific conditions, these states even exhibit the potential to approach or saturate the ultimate Heisenberg limit. This review offers a comprehensive overview of the theoretical underpinnings, representative preparation methodologies, experimental progress and emerging applications of non-Gaussian states in quantum metrology. Special attention is devoted to illustrating their transformative potential for the development of next-generation quantum sensors and high-precision measurement instruments, while also addressing prevailing challenges and delineating promising future research trajectories in this rapidly advancing field.