Weak Measurements

Miguel Orszag

Lan E Luo, Tong Li, Tianchen Li +3 more

In the application of weak measurements, such as the estimation of magnetic parameters, the purely real weak coupling of standard weak measurement (SWM) does not correspond to the true physical parameters. To accommodate more complex application scenarios, we further explore three different weak measurement models in which both complex weak coupling and complex weak values coexist. This paper theoretically analyzes pointer variations and applicable ranges in SWM, double pointer weak measurement (DPWM), and almost-balanced weak measurement (ABWM) under specific conditions. Notably, only ABWM can successfully distinguish the real and imaginary components of weak values under complex weak-coupling conditions. While SWM and DPWM can also solve for weak values, they fail to obtain a unique and correct test value. The ABWM technique provides a higher sensitivity than SWM when measuring extremely small parameters. Furthermore, we apply ABWM to the magneto-optical Kerr effect measurement of a Ni-Fe film. This research deepens the understanding of weak measurement techniques and introduces new methods for multiparameter measurements.

Víctor M. Acosta

Kazuhisa Ogawa, Osamu Yasuhiko, Hirokazu Kobayashi +2 more

Weak values are typically obtained experimentally by performing weak measurements, which involve weak interactions between the measured system and a probe. However, the determination of weak values does not necessarily require weak measurements, and several methods without weak system-probe interactions have been developed previously. In this work, a framework for measuring weak values is proposed to describe the relationship between various weak value measurement techniques in a unified manner. This framework, which uses a probe-controlled system transformation instead of the weak system-probe interaction, improves the understanding of the currently used weak value measurement methods. Furthermore, a diagrammatic representation of the proposed framework is introduced to intuitively identify the complex values obtained in each measurement system. By using this diagram, a new method for measuring weak values with a desired function can be systematically derived. As an example, a scan-free and more efficient direct measurement method of wavefunctions than the conventional techniques using weak measurements is developed.

Lev Vaidman A

Shengshi Pang, Shengjun Wu, Zeng‐Bing Chen

Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the preselection and the postselection should not be too small generally. In this work, we study the weak measurement on a qubit system with exactly or asymptotically orthogonal pre- and postselections. We shall establish a general rigorous framework for the weak measurement beyond the weak value formalism, and obtain the average output of a weak measurement when the pre- and postselections are exactly orthogonal. We shall also study the asymptotic behavior of a weak measurement in the limiting process that the pre- and postselections tend to be orthogonal.