As an essential component of state-of-the-art quantum technologies, fast and efficient quantum measurements are in persistent demand over time. We present a proof-of-principle experiment on a new dimensionless pseudo-spin pointer based on weak measurement. In the context of optical parameter estimation, we demonstrate that the parametric distribution's moment is obtained experimentally by employing the dimensionless pointer without measuring the distribution literally. In addition to the sheer liberation of experimental expense, the photon-countering-based pointer is well-calibrated for the detection of weak signals. We show that for signals $3$-$4$ orders of weaker in strength than the area-array camera method, an order of improvement in precision is achieved experimentally.
Quantum metrology is being gradually studied for weak measurement systems. For weak measurement systems with thermal state pointer, we find that in the displacement space corresponding to imaginary weak values, the maximal QFI after successful postselection can attain the level of thermal fluctuations, without surpassing total QFI, and that QFI which increases with increasing temperature can constantly improve the measurement precision. These results are much better than that of weak measurement with pure state (i.e., Gaussian state) pointer. On the other hand, in Kerr nonlinear interaction sy…
Exploring high sensitivity on the measurement of angular rotations is an outstanding challenge in optics and metrology. In this work, we employ the mn-order Hermite-Gaussian beam in the weak measurement scheme with an angular rotation interaction, where the rotation information is taken by another HG mode state completely after the post-selection. By taking a projective measurement on the final light beam, the precision of angular rotation is improved by a factor of 2mn+m+n. For verification, we perform an optical experiment where the minimum detectable angular rotation improves $\sqrt{15}$-fo…
In this study, we investigate the advantages of non-classical pointer states in the generalized modular value scheme. We consider a typical von Neumann measurement with a discrete quantum pointer, where the pointer is a projection operator onto one of the states of the basis of the pointer Hilbert space. We separately calculate the conditional probabilities, Q_{M} factors, and signal-to-noise ratios of quadrature operators of coherent, coherent squeezed, and Schrödinger cat pointer states and find that the non-classical pointer states can increase the negativity of the field and precision of m…
In this work, the measurement transition as well as precision measurement advantages of single-photon-added coherent state after postselected von Neumann measurement are investigated. We noticed that the weak-to-strong measurement transition characterized by the shifts of pointer's position and momentum variables occurred in continuously by controlling a dimensionless parameter associated with system-pointer coupling. We calculate the ratio between the signal-to-noise ratio of nonpostselected and postselected measurements, and the latter is used to find the quantum Fisher information. We found…
We investigate, within the weak measurement theory, the advantages of non-classical pointer states over semi-classical ones for coherent, squeezed vacuum, and Schröinger cat states. These states are utilized as pointer state for the system operator $\hat{A}$ with property $\hat{A}^{2}=\hat{I}$, where $\hat{I}$ represents the identity operator. We calculate the ratio between the signal-to-noise ratio (SNR) of non-postselected and postselected weak measurements. The latter is used to find the quantum Fisher information for the above pointer states. The average shifts for those pointer states wit…
Pre- and post-selected (PPS) measurement, especially the weak PPS measurement, is a useful protocol for amplifying small physical parameters. However, it is difficult to retain both the attainable highest measurement sensitivity and precision with the increase of the parameter to be measured. Here, a modulated PPS measurement scheme based on coupling-strength-dependent modulation is presented with the highest sensitivity and precision retained for an arbitrary coupling strength. This idea is demonstrated by comparing the modulated PPS measurement scheme with standard PPS measurementv scheme, r…
Pointer states are long-lasting high-fidelity states in open quantum systems. We show how any pure state in a non-Markovian open quantum system can be made to behave as a pointer state by suitably engineering the coupling to the environment via open-loop periodic control. Engineered pointer states are constructed as approximate fixed points of the controlled open-system dynamics, in such a way that they are guaranteed to survive over a long time with a fidelity determined by the relative precision with which the dynamics is engineered. We provide quantitative minimum-fidelity bounds by identif…
Photonic spin Hall effect (SHE) holds great potential applications in precision metrology. How to obtain a high measurement precision is an important issue to detect the photonic SHE. In this letter, we propose using optimal preselection and postselection in weak measurements to enhance the measurement precision. We find that the maximum weak value and pointer shift can be obtained with an optimal overlap of preselection and postselection states. These findings offer the possibility for improving the precision of weak measurements and thereby have possible applications for accurately character…
Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising resu…
High-sensitivity and high-resolution collaborative determination of birefringence coefficient using weak measurement
Taiyuan University of Technology（太原理工大学）；Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology（先进换能器与智能控制系统教育部重点实验室，太原理工大学）；College of Physics and Optoelectronics, Taiyuan University of Technology（太原理工大学物理与光电学院）；Shanxi Key Laboratory of Precision Measurement Physics, Taiyuan University of Technology（太原理工大学山西省精密测量物理重点实验室）
In contrast to the standard quantum state tomography, the direct tomography seeks the direct access to the complex values of the wave function at particular positions (i.e., the expansion coefficient in a fixed basis). Originally put forward as a special case of weak measurement, it can be extended to arbitrary measurement setup. We generalize the idea of "quantum metrology," where a real-valued phase is estimated, to the estimation of complex-valued phase, and apply it for the direct tomography of the wave function. It turns out that the reformulation can help us easily find the optimal measu…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run into difficulties of one sort or another. One of the first detailed descriptions was given by Sudarshan and his collaborators who, motivated by the measurement problem in quantum mechanics, proposed a Hilbert space formulation of classical-quantum interactions which made use of the Koopman-von Neumann description of classical systems. Here we use the approach …
The fact that not all quantum observables are jointly measurable is one of the major differences between quantum and classical theory. In the former, non-commuting observables can only be simultaneously measured with limited precision. We report on an experimental implementation of such a simultaneous measurement of two non-commuting observables based on the framework of weak von Neumann measurements. We use a photonic setup where the polarisation degree of freedom acts as the system and the two components of the transversal position correspond to the pointers of the measurement apparatuses. I…
The measurement process in quantum mechanics is usually described by the von Neumann projection postulate, which forms a basic constituent of the laws of quantum mechanics. Since this postulate requires the outside observer of the system, it is hard to apply quantum mechanics to the whole Universe. Therefore we propose that the quantum measurement process is actually a physical process associated with the ubiquitous mechanism of spontaneous symmetry breaking. Based on this proposal, we construct a quantum measurement model in which the von Neumann projection is described as the dynamical pro-c…
We show that in wavepacket tunnelling localisation of the transmitted particle amounts to a quantum measurement of the delay it experiences in the barrier. With no external degree of freedom involved, the envelope of the wavepacket plays the role of the initial pointer state. Under tunnelling conditions such 'self measurement' is necessarily weak, and the Hartman effect just reflects the general tendency of weak values to diverge, as post-selection in the final state becomes improbable. We also demonstrate that it is a good precision, or 'not really weak' quantum measurement: no matter how wid…
Weak-value amplification (WVA) has recently become an important technique for parameter estimation, owing to its ability to enhance the signal-to-noise ratio by amplifying extremely small signals with proper postselection strategies. In this paper, we propose an adaptive WVA scheme to achieve the highest Fisher information when using an unbalanced pointer. Different from previous schemes, the adaptive WVA scheme is associated with a real-time update on the postselection states with the help of feedback information from the outcomes, and the "extremely small" condition set on the parameter of i…
The extraordinary concept of weak value amplification has attracted considerable attention for addressing foundational questions in quantum mechanics and for metrological applications in high precision measurement of small physical parameters. Here, we experimentally demonstrate a fundamental relationship between the weak value of an observable and complex zero of the response function of a system by employing weak value amplification of spin Hall shift of a Gaussian light beam. Using this relationship, we show that arbitrarily large weak value amplification far beyond the conventional weak me…
