This thesis aims to help in bridging the gap between the ideals of theoretical quantum metrology and its practical application. We take three major approaches to achieving this aim: to investigate the effect of noise on metrological schemes, to study the role of resources and to devise ways to engineer effective probe states from experimentally feasible elements. We find that noise is detrimental to measurement precision but that this may be overcome by thinking outside of the asymptotic regime. Considering resources, whilst entanglement may provide an advantage, it is only useful in limited circumstances and even in this case a very small entangled state may perform as well as a large one. This is also true in multiparameter metrology, where we find that it is possible for the simultaneous estimation of phase and noise to be advantageous, even when the parameters are not fully compatible. We discuss strategies for multiparameter estimation in both discrete and continuous variable formalisms. In the continuous variable formalism, we go beyond the consideration of entanglement as a resource and construct a generalised resource theory for Gaussian states and operations which has particular cases in entanglement, steerability and squeezing. We provide a measure for this resource as well as a no-go theorem for its distillation. Finally, we use a genetic algorithm to devise state engineering schemes to produce highly sensitive states for quantum metrology.
This thesis aims to help in bridging the gap between the ideals of theoretical quantum metrology and its practical application. We take three major approaches to achieving this aim: to investigate the effect of noise on metrological schemes, to study the role of resources and to devise ways to engineer effective probe states from experimentally feasible elements. We find that noise is detrimental to measurement precision but that this may be overcome by thinking outside of the asymptotic regime. Considering resources, whilst entanglement may provide an advantage, it is only useful in limited circumstances and even in this case a very small entangled state may perform as well as a large one. This is also true in multiparameter metrology, where we find that it is possible for the simultaneous estimation of phase and noise to be advantageous, even when the parameters are not fully compatible. We discuss strategies for multiparameter estimation in both discrete and continuous variable formalisms. In the continuous variable formalism, we go beyond the consideration of entanglement as a resource and construct a generalised resource theory for Gaussian states and operations which has particular cases in entanglement, steerability and squeezing. We provide a measure for this resource as well as a no-go theorem for its distillation. Finally, we use a genetic algorithm to devise state engineering schemes to produce highly sensitive states for quantum metrology.
Quantum metrology aims to exploit quantum phenomena to overcome classical limitations in the estimation of relevant parameters. We consider a probe undergoing a phase shift $\ensuremath{\varphi}$ whose generator is randomly sampled according to a distribution with unknown concentration $\ensuremath{\kappa}$, which introduces a physical source of noise. We then investigate strategies for the joint estimation of the two parameters $\ensuremath{\varphi}$ and $\ensuremath{\kappa}$ given a finite number N of interactions with the phase imprinting channel. We consider both single qubit and multipartite entangled probes, and identify regions of the parameters where simultaneous estimation is advantageous, resulting in up to a twofold reduction in resources. Quantum enhanced precision is achievable at moderate N, while for sufficiently large N classical strategies take over and the precision follows the standard quantum limit. We show that full-scale entanglement is not needed to reach such an enhancement, as efficient strategies using significantly fewer qubits in a scheme interpolating between the conventional sequential and parallel metrological schemes yield the same effective performance. These results may have relevant applications in optimization of sensing technologies.
Nature imposes fundamental limits on how precisely we can probe the physical world. Quantum metrology is the study of achieving higher precision and accuracy in estimating the physical parameters by harnessing quantum resources. It is considered one of the most promising quantum technologies, offering significant advantages over classical ones in both near‑term and long‑term applications. However, existing theoretical research in quantum metrology often falls short of providing a unified and rigorous understanding of the ultimate precision under realistic experimental limitations on available quantum resources. In this thesis, we conduct a systematic investigation of the optimal precision limits in quantum metrology and identify the metrological strategies that achieve optimality under specified resource constraints. We primarily focus on the single-parameter estimation of quantum processes, a cornerstone task in quantum metrology. We first establish a general framework of strictly optimal quantum metrology using semidefinite programming within the formalism of higher-order quantum operations. This framework reveals a strict hierarchy for the performance of different families of strategies---parallel, sequential, and indefinite-causal-order ones---each subject to specific causal constraints. Our results rigorously demonstrate a quantum metrological advantage of indefinite causal order in finite-dimensional systems, which has recently aroused rapidly growing interest. In realistic scenarios, a fully optimized quantum metrology protocol may be experimentally demanding due to the complexity of state preparation and control. Tailored to practical constraints on the allowed ancilla and control operations, we propose a highly efficient tensor network algorithm to optimize the probe state and a long sequence of control for quantum metrology. When the number of control steps tends to infinity, we develop an asymptotic theory of quantum metrology for achieving the ultimate precision limit---Heisenberg limit---without ancilla. This contrasts with the traditional approach using quantum error correction for metrology that typically requires noiseless and controllable ancilla. Our results pave the way for exploiting the full potential of quantum resources in metrology. In the near term, our methods enable high-precision estimation with limited interaction with the unknown process using experimentally feasible control techniques. In the long term, they lay the foundation for scalable and fault-tolerant quantum metrology.
Recent years have witnessed a growing interest in understating the limitations imposed by quantum noise in precision measurements and devising techniques to reduce it. The attention is currently turning to the simultaneously estimation of several parameters of interest, driven by its promising potential across a wide range of sensing applications as well as fueled by experimental progress in various optical and atomic platforms. Here, we provide a comprehensive overview of key research directions in multiparameter quantum sensing and metrology, highlighting both opportunities and challenges. We introduce the basic framework, discuss ultimate sensitivity bounds, optimal measurement strategies, and the role of quantum incompatibility, showing important differences with respect to single-parameter estimation. Additionally, we discuss emerging experimental implementations in distributed quantum sensing, including cutting-edge optimization techniques. This review aims to bridge the gap between theory and experiments, paving the way for the next-generation of quantum sensors and their integration with other quantum technologies.
This thesis explores various protocols which can be applied to quantum metrology, such that precision of the measurement can beat the best classical approaches. We first demonstrate that ancilla-assisted schemes can improve phase estimation in the presence of noise, and we propose an experiment to demonstrate these effects. Given that the use of ancillae helps, it is no surprise that there are noisy channels for which the optimal strategy may depend on the noise level. We show that there is a non-trivial crossover between the ancilla-assisted strategy and the parallel-entangled strategy for Pauli noise channels and the amplitude damping channel. We see that under certain circumstances, the environment cannot access the parameter of interest. We then integrated techniques from quantum communication, to derive a general framework that renders quantum metrology protocols into cryptographic ones. Here the protocol is unconditionally secure if the trusted parties wish only to achieve the standard quantum limit. If Heisenberg-limited precision is to be achieved, they sacrifice some security, where adversaries can access information, but only at the risk of getting caught at it (cheat-sensitivity). In many scenarios, the quantum Fisher information is achieved for only one value of the phase. In a particular phase estimation scheme that measures the parity at the output of a Mach-Zehnder interferometer where the input is a two-mode squeezed vacuum, this problem is particularly imminent. We apply an adaptive technique to resolve this issue, showing that one can achieve precisions substantially below the shot noise limit. The key to a quadratically enhanced improvement in quantum metrology is entanglement. Finally, we demonstrate in a photonic system how high-dimensional entanglement can be certified, and provide an alternate interpretation of entanglement from an information-theoretic perspective.
Cubic phase states provide the essential non-Gaussian resource for continuous-variable quantum computing. We show that they also offer significant potential for quantum metrology, surpassing the phase-sensing sensitivity of all Gaussian states at equal average photon number. Optimal sensitivity requires only moderate initial squeezing, and the non-Gaussian advantage remains robust against loss and detection noise. We identify optimal measurement strategies and show that several experimentally relevant preparation schemes surpass Gaussian limits, in some cases reaching the sensitivity of cubic phase states. Our results establish cubic phase states as a promising resource for quantum-enhanced precision measurements beyond Gaussian limits.
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and the design of optimized measurement observables. We discuss precision limits and optimal strategies in quantum metrology and sensing with a single mode of quantum continuous variables. We focus on the practically most relevant cases of estimating displacements and rotations and provide the sensitivities of the most important classes of states that includes Gaussian states and superpositions of Fock states or coherent states. Fundamental precision limits that are obtained from the quantum Fisher information are compared to the precision of a simple moment-based estimation strategy based on the data obtained from possibly sub-optimal measurement observables, including homodyne, photon number, parity and higher moments. Finally, we summarize some of the main experimental achievements and present emerging platforms for continuous-variable sensing. These results are of particular interest for experiments with quantum light, trapped ions, mechanical oscillators, and microwave resonators.