To describe the pre- and post-selected quantum ensembles, a complex quantity called the weak value of an operator is used. The weak value is highly controversial due to the fact that it is not bounded by the possible eigenvalues of the corresponding operator. Nevertheless, the obtaining of the anomalous weak value is regarded as a powerful technique in the quantum interferometry nowadays. Here it is shown that the postselection on a quantum system recovers a completely hidden interference effect in the measurement apparatus. Studying the interference pattern shows the optimal settings for the amplification and the parameter estimation. It also proves that the weak value is not an element of reality. Using single photons, it is investigated how a postselected photon can impart a $π$ phase shift (the peak of the amplification) to a photon interacting weakly with it in a nonlinear optical medium. The increasing of the degree of the entanglement lies behind the effectiveness of the postselection in the parameter estimation. In particular, arranging to postselect on pure entangled states can optimize the signal-to-noise ratio, allowing to achieve high-sensitive measurements using low input power.
Interactions of pre- and postselected quantum particles
Tel-Aviv University（特拉维夫大学）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Ludwig-Maximilians-Universität（路德维希-马克西米利安大学）；Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität（慕尼黑数学哲学中心，路德维希-马克西米利安大学）；Korea Institute for Advanced Study（韩国高等研究院）；Chapman University（查普曼大学）
In conventional measurement, to reach the greatest accuracy of parameter estimation, all samples must be measured since each independent sample contains the same quantum Fisher information. In postselected metrology, postselection can concentrate the quantum Fisher information of the initial samples into a tiny post-selected sub-ensemble. It has been proven that this quantum advantage can not be realized in any classically commuting theory. In this work, we present that the advantage of postselection in weak value amplification (WVA) can not be achieved without quantum coherence. The quantum c…
Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror's position displacement of one photon. In the WVA regime (Weak Value Amplification regime), the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror's position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the co…
We experimentally demonstrate that when three single photons transmit through two polarization channels, in a well-defined pre- and postselected ensemble, there are no two photons in the same polarization channel by weak-strength measurement, a counter-intuitive quantum counting effect called quantum pigeonhole paradox. We further show that this effect breaks down in second-order measurement. These results indicate the existence of quantum pigeonhole paradox and its operating regime.
Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with negative quasiprobabilities -- quantum extensions of probabilities -- engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using P…
NV-ensemble enabled microwave/NV parametric amplifier with optimal driving
Akhiezer Institute for Theoretical Physics, NSC KIPT（阿赫伊泽尔理论物理研究所，NSC KIPT）；U.S. Army DEVCOM Army Research Laboratory（美国陆军DEVCOM陆军研究实验室）；University of Massachusetts at Boston（波士顿马萨诸塞大学）；Education and Research Institute “School of Physics and Technology”, Karazin Kharkiv National University（克拉辛哈尔科夫国立大学“物理与技术学院”教育与研究所）；Massachusetts Institute of Technology（麻省理工学院）；Tulane University（杜兰大学）
State preparation via postselected weak measurement in three wave mixing process is studied. Assuming the signal input mode prepared in a vacuum state, coherent state or squeezed vacuum state, separately, while the idler input prepared in weak coherent state and passing the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of idler beam's path, the signal output channel is prepared in single-photon Fock state, single-photon-added coherent state or single-photon-added squeezed vacuum state with ve…
Preselection-Encoded Weak-Value Interferometry for Optical-Rotation Metrology
Zhejiang University of Technology（浙江工业大学）；University of Science and Technology of China（中国科学技术大学）；Zhejiang University of Science and Technology（浙江科技学院）
Ensemble Engineering to Overcome Destructive Cancellation in Quantum Measurements
Purdue University（普渡大学）；North Carolina State University（北卡罗来纳州立大学）；National Center for Computational Sciences, Oak Ridge National Laboratory（橡树岭国家实验室国家计算科学中心）
