Abstract Post-selected measurement is used as a fundamental axiom in quantum optics. Here, a standard model of post-selected measurement with the input coherent pointer state is considered and the influence of weak value parameters on the quantum phase distribution function is studied on the basis of some analytical calculations. On the other hand, the effects of post-selected measurement on quantum phase fluctuations of the input coherent pointer states have been investigated, where the Barnett-Pegg formalism for the measured phase operators is assumed. It has been observed that the quantum phase fluctuations depend on some parameters such as the coupling strength, average value of input photon number, phase angle of the input coherent pointer state and two fundamental parameters of the complex weak value. Lastly, the presence of nonclassical effect is also checked for different parameters of quantum phase fluctuations.
Abstract Post-selected measurement is used as a fundamental axiom in quantum optics. Here, a standard model of post-selected measurement with the input coherent pointer state is considered and the influence of weak value parameters on the quantum phase distribution function is studied on the basis of some analytical calculations. On the other hand, the effects of post-selected measurement on quantum phase fluctuations of the input coherent pointer states have been investigated, where the Barnett-Pegg formalism for the measured phase operators is assumed. It has been observed that the quantum phase fluctuations depend on some parameters such as the coupling strength, average value of input photon number, phase angle of the input coherent pointer state and two fundamental parameters of the complex weak value. Lastly, the presence of nonclassical effect is also checked for different parameters of quantum phase fluctuations.
Weak measurement has ignited extensive research and discussions in the field of quantum metrology due to its sufficient potential in quantum measurement applications. Recent studies demonstrate that weak measurement protocols, when integrated with quantum resources, can achieve Heisenberg scaling while maintaining technical noise advantages. However, scenarios involving dephasing noise have not been addressed, as such noise induces rapid degradation of Heisenberg scaling to the standard quantum limit. Here, we incorporate phase fluctuations, a typical dephasing noise, into three Heisenberg-scaling systems. We find that postselection invariably reduces the robustness of quantum systems. Compared to coherent pointer states, squeezed coherent pointer states can exhibit superior resilience against phase fluctuations through appropriate squeezing-parameter optimization. In addition, in entanglement-assisted systems, we can optimize the postselected angle to compensate for Fisher information loss induced by the postselection process. Our findings reveal that weak measurement exhibits inherent limitations in dephasing noise metrology compared to conventional measurement.
Nonclassical features of the pointer states in the q-deformed post-selected weak measurement
We study q-deformed coherent states of the Arik-Coon harmonic oscillator as the quantum resource in the post-selected weak measurement. First, we show how the precision of weak measurement is improved significantly due to q-deformation. Next, we focus on the role of the interplay between the deformation parameter and the interaction strength on the nonclassical nature of light. In particular, we show that sub-Poissonian photon distribution as characterized by Mandel parameter, photon antibunching effect, and quadrature squeezing are greatly enhanced by q-deformation. Our results not only advance the understanding of the fundamentals of q-deformed quantum mechanics, but also raise the potential to contribute to quantum technologies.
Exact pointer states are obtained for projection operator measurements performed upon pre-selected (PS) and upon pre- and post-selected (PPS) quantum systems. These states are used to provide simple exact expressions for both the pointer spatial probability distribution profiles and the mean values of arbitrary pointer observables associated with PS and PPS projection operator measurements that are valid for any strength of the interaction which couples a measurement pointer to the quantum system. These profiles and mean values are compared in order to identify the effects of post-selection upon projector measurement pointers. As a special case, these mean value results are applied to the weak measurement regime - yielding PS and PPS mean value expressions which are valid for any operator (projector or non-projector). Measurement sensitivities which are useful for estimating weak measurement accuracies for PS and PPS systems are also obtained and discussed.
We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre- and post-selected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.
We investigate the phase fluctuations of the input coherent light coupled to a quantum driven harmonic oscillator with time-dependent mass and frequency (DHTDMF). Under the Barnett–Pegg formalism, we calculate the phase fluctuation parameters U, Q, and S as functions of interaction time, coupling strength, intensity and phase of the input coherent light. In order to make the analytical studies feasible, we use ω(t) = ω(0) = ω, , and the periodically driven term . For far off-resonance condition (i.e. or ), the driven term hardly affects the phase fluctuation parameters U, Q, and S. The exact analytical expressions for the phase fluctuation parameters for various special cases are exhibited. The effects of vacuum field on the fluctuations of the phase parameters are clearly indicated. In order to have a sense for these analytical results, we give symbolic calculations for a few special situations. Even for the on-resonance condition , the effects of the driven term are negligible for low damping constant γ. Interestingly, for the strong input field, the values of the phase fluctuation parameters are independent of the intensity of the input field. For high intensity of the input field, low damping constant and for far off-resonance condition, the phase fluctuation parameters U, S and Q exhibit an increase and decrease compared to their initial values (i.e. t = 0). All possible cases of physical interest are also investigated. In particular, the effects of input vacuum field on the phase fluctuation parameters are discussed in detail. The phase of the input coherent light plays an important role in the calculations of the phase fluctuation parameters.
We investigate, within the weak measurement theory, the advantages of nonclassical pointer states over semiclassical ones for coherent, squeezed vacuum, and Schr\"odinger cat states. These states are utilized as pointer states for the system operator $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}$ with property ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}}^{2}=\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{I}$, where $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{I}$ represents the identity operator. We calculate the ratio between the signal-to-noise ratio of nonpostselected 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 with arbitrary interaction strength are investigated in detail. One key result is that we find the postselected weak measurement scheme for nonclassical pointer states to be superior to semiclassical ones. This can improve the precision of the measurement process.