Quantum metrology is a subfield of quantum information science that seeks to enhance measurement precision by exploiting quantum phenomena. This thesis presents three experimental investigations that are related to quantum metrology.The first experiment demonstrates a quantum-inspired sub-Rayleigh parameter estimation technique capable of resolving the separation and relative intensities of two incoherent light sources, positioned closer than the Rayleigh criterion. The method relies solely on passive linear optical components, making it readily implementable in standard optical laboratories without specialized equipment. The second experiment demonstrates a scalable protocol for compressing the quantum Fisher information of an arbitrarily large ensemble of identical quantum states into a single quantum state. As a proof of concept, we implement its simplest building block by compressing the quantum Fisher information contained in two qubits into a single qubit. The third experiment demonstrates that entangled probes can optimally estimate the strength of a dephasing channel, including the case where the dephasing axis is unknown.Together, these experiments provide examples of the capabilities of quantum metrology and offer new implementation ideas.
Quantum metrology is a subfield of quantum information science that seeks to enhance measurement precision by exploiting quantum phenomena. This thesis presents three experimental investigations that are related to quantum metrology.The first experiment demonstrates a quantum-inspired sub-Rayleigh parameter estimation technique capable of resolving the separation and relative intensities of two incoherent light sources, positioned closer than the Rayleigh criterion. The method relies solely on passive linear optical components, making it readily implementable in standard optical laboratories without specialized equipment. The second experiment demonstrates a scalable protocol for compressing the quantum Fisher information of an arbitrarily large ensemble of identical quantum states into a single quantum state. As a proof of concept, we implement its simplest building block by compressing the quantum Fisher information contained in two qubits into a single qubit. The third experiment demonstrates that entangled probes can optimally estimate the strength of a dephasing channel, including the case where the dephasing axis is unknown.Together, these experiments provide examples of the capabilities of quantum metrology and offer new implementation ideas.
In quantum metrology, a major application of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cramér-Rao bound. Yet, the latter fails to completely characterize the distribution of estimates in the nonasymptotic regime. Optimizing metrology protocols with respect to the Cramér-Rao bound can therefore lead to surprisingly poor finite-sample performance. This can be avoided by quantifying the quality of a metrology protocol by the probability of obtaining an estimate with a given accuracy. Using this intrinsically single-shot quantity naturally accommodates the finite-sample regime. We show that the fundamental limits of this figure of merit can be quantified through a multihypothesis testing problem between quantum states. Building on this connection, we derive an analogue of the Cramér-Rao bound that contains explicit corrections relevant to the finite-sample regime. We apply the finite-sample metrology framework to the example task of phase estimation with an ensemble of spin-1/2 particles, giving unambiguous evidence that large quantum Fisher information does not guarantee that a metrology protocol has a good finite-sample performance. Overall, analyzing the probability of success allows the reliable study of quantum metrology in the finite-sample regime and opens up a plethora of new avenues for research at the interface of quantum information theory and quantum metrology.
The fundamental precision limit of an interferometer is crucial since it bounds the best possible sensitivity one could achieve using such a device. This thesis will focus on several different interferometers and try to give the ultimate precision bounds by carefully counting all the resources used in the interferometers. The thesis begins with the basics of the quantum state of light. The fundamentals of quantum metrology are also reviewed and discussed. More specifically, the terminology of classical and quantum Cram\'er-Rao bound and classical and quantum Fisher information are introduced. Chapter 3 discusses the conclusive precision bounds in two-mode interferometer such as Mach-Zehnder interferometer (MZI) and SU(1,1) interferometer. I revisit the quantum Fisher information approach of these two interferometers and show the discrepancy of phase sensitivity on the physically same setup. Then I establish fundamental precision estimation bounds for such device, due to the reason that many works of literature fail to accurately count the resources and knowledge of phase-to-be-estimated used in the interferometers. The analysis suggests that for a MZI, one can never do better than SNL in phase sensitivity, when an input to one of the two ports is the vacuum. If one does not allow the detector to use any external phase reference or power resource, then the precision is limited by the SNL. For a SU(1,1) interferometer, firstly, when one of the input states is restricted to be a vacuum state, I showed that by using either the phase-averaging method or the quantum Fisher information matrix method, different phase configurations of the SU(1,1) interferometer result in the same QFI. Secondly, I compared the results of the phase-averaging method and the quantum Fisher information matrix method, and then I argued that for an SU(1,1) interferometer, phase averaging or quantum Fisher information matrix method is generally required, and they are equivalent. Finally, I used the quantum Fisher information matrix method to calculate the precision limit for other common input states, such as two coherent state inputs or coherent state with squeezed vacuum inputs. In chapter 4, I will consider a passive multi-mode interferometer for multiparameter phase estimation. It was suggested that optical networks with relatively inexpensive overhead---single photon Fock states, passive optical elements, and single photon detection---can show significant improvements over classical strategies for single-parameter estimation, when the number of modes in the network is small. In this chapter, I analytically compute the quantum Cramer-Rao bound to show these
Optical quantum metrology uses specially-prepared states of light to probe sensitive samples. Choosing a suitable probe state allows one to extract more information per probe photon about an unknown parameter than is possible using any classical technique. In effect, these techniques improve the sensitivity of the measurement whenever the number of probe photons is constrained in some way. This thesis presents experimental and theoretical results on the use of pairs of time-frequency entangled photons in precision measurements. It begins with an overview of necessary background knowledge about quantum optics and quantum information. This is followed by a theoretical discussion on the estimation of a single delay using two-photon interference. We show that constraints on the probe photon's bandwidth complicate the measurement problem, requiring suitable optimization of the two-photon quantum state to avoid losing precision. We then consider the use of two-photon interference for linear spectroscopic measurements. Linear spectroscopy relates the absorption and phase spectrum of a sample to unknown electronic parameters. We describe a proof-of-principle experiment demonstrating that two-photon interferometric spectroscopy can be used for simultaneously measurement of both absorption and phase. This is followed by an information-theoretic discussion of the precision of this technique. For low losses, we show that the method provides phase sensitivity similar to classical interferometry while approaching the optimal absorption precision of any possible measurement. If the absorption and phase values are both related to a single unknown parameter, then our technique provides improved sensitivity to this parameter compared to both classical measurements and other quantum techniques in the presence of realistic levels of loss. We conclude with a discussion of quantum-optical coherence tomography, which is a two-photon interferometric method for determining the material structure of a sample. We present an ongoing experiment which aims to apply the method to tissue-like samples, where the quantum measurement is limited by a poor signal-to-noise ratio. Preliminary results demonstrate that this noise can be largely reduced by suitable frequency-domain filtering. This allows us to precisely determine the position of a scattering center using a few hundred detected photon pairs despite the presence of large amounts of noise. We follow this with a theoretical discussion of signal artifacts which are known to complicate the measured interferogram. We show these artifacts are due to a distinct interferometric effect, which can be distinguished from the signal of interest using the relative time delay between detected photons. We conclude with a brief discussion on possible techniques for artifact removal.
Fisher information plays a central role in statistics and quantum metrology, providing the basis for the celebrated Cramér-Rao bound. In this work, we introduce a new information measure based on higher-order Fisher information and show that it naturally leads to a generalized uncertainty relation for parameter estimation, which can be regarded as an extension of the Cramér-Rao bound. As an application, we analyze the case of quantum phase estimation with a single qubit and compare our theoretical bounds with the well-known established hierarchical bounds. Finally, we experimentally validate the proposed framework using a photonic platform.
The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical resources. Theoretically, the fundamental minimum uncertainty in the estimation of a parameter for a given probing state is bounded by the quantum Cramér-Rao bound. From a practical perspective, it is necessary to find physical measurements that can saturate this fundamental limit and to show experimentally that it is possible to perform measurements with the required precision to do so. Here we perform experiments that saturate the quantum Cramér-Rao bound for transmission estimation over a wide range of transmissions when probing the system under study with a continuous wave bright two-mode squeezed state. To properly take into account the imperfections in the generation of the quantum state, we extend our previous theoretical results to incorporate the measured properties of the generated quantum state. For our largest transmission level of 84%, we show a 62% reduction over the optimal classical protocol in the variance in transmission estimation when probing with a bright two-mode squeezed state with -8 dB of intensity-difference squeezing. Given that transmission estimation is an integral part of many sensing protocols, such as plasmonic sensing, spectroscopy, calibration of the quantum efficiency of detectors, etc., the results presented promise to have a significant impact on a number of applications in various fields of research.
Quantum measurement plays a crucial role in quantum metrology. Due to the limitations of experimental capabilities, collectively measuring multiple copies of probing systems can present significant challenges. Therefore, the concept of locality in quantum measurements must be considered. In this work, we investigate the possibility of achieving the quantum Cramér-Rao bound (QCRB) through local measurements (LMs). We first demonstrate that if there exists a LM to saturate the QCRB for qubit systems, then we can construct another rank-1 local projective measurement to saturate the QCRB. In this sense, rank-1 local projective measurements are sufficient to analyze the problem of saturating the QCRB. For pure qubits, we propose two necessary and sufficient methods to determine whether and how a given parameter estimation model can achieve the QCRB through LMs. The first method, dubbed the iterative matrix partition method and based on unitary transformations that render the diagonal entries of a traceless matrix vanish, elucidates the underlying mathematical structure of LMs as well as the local measurements with classical communications (LMCC), generalizing the result by Zhou . [], which only holds for the later case. We clarify that the saturation of the QCRB through LMs for the Greenberger–Horne–Zeilinger-encoded states is actually due to the self-similar structure in this approach. The second method, dubbed the hierarchy of orthogonality conditions and based on the parametrization of rank-1 measurements for qubit systems, allows us to construct several examples of saturating QCRBs, including the three-qubit W states and the N -qubit W states ( N ≥ 3 ). Our findings offer insights into achieving optimal performance in quantum metrology when measurement resources are limited.