Elucidation of dynamics of weak values as physical quantities from the viewpoint of fluctuation and time evolution

2020 Fiscal Year Final Research Report

• Project/Area Number: 19K14606
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Hokkaido University
• Principal Investigator: Ogawa Kazuhisa 北海道大学, 情報科学研究院, 助教 (80772574)
• Project Period (FY): 2019-04-01 – 2021-03-31
• Keywords: 弱測定 / 弱値

Outline of Final Research Achievements

The variance of an observable in a pre-selected quantum system appears as an increase in the probe wave packet width in indirect measurements. Extending this framework to pre- and post-selected systems, we formulate a complex-valued counterpart of the variance called "weak variance." In our formulation, the real and imaginary parts of the weak variance appear as changes in the probe wave packet width in the vertical-horizontal and diagonal-antidiagonal directions, respectively, on the quadrature phase plane. Using an optical system, we experimentally demonstrate these changes in the probe wave packet width. Furthermore, we show that the weak variance can be expressed as the variance of the weak-valued probability distribution in pre- and post-selected systems. These operational and statistical interpretations support the rationality of formulating the weak variance as a complex counterpart of the variance in pre- and post-selected systems.

Free Research Field

量子光学、量子情報

Academic Significance and Societal Importance of the Research Achievements

量子系に対する測定結果は一般的に確率的に揺らぎ、これは古典力学には見られない量子に本質的な性質である。本研究はこの量子系に対する測定に伴う揺らぎの概念を精緻化・一般化したものである。つまり、事前・事後選択した量子系には本来的に複素数で表される揺らぎ（弱分散）が備わっており、事後選択しない場合はそれらの確率混合として通常の非負の分散が現れる。そしてそのような複素数の揺らぎは、実験的にも観測できたことから、現実的に利用可能な量であることが示された。本研究により、事前・事後選択が関係する量子パラドックスの解決に重要な知見を与え、また逆に弱分散の制御によって波動関数を成形する新たな手段が与えられる。