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ハイゼンベルクの不確定性関係、というたいへん基本的な事柄についての論文を小川くんと書きました。読んで！
量子力学を勉強中の学部生が読んでも面白いと思うのでそういう人も是非、感想きかせてもらえると嬉しいです。
https://arxiv.org/abs/2403.19440
arXiv.orgGaussian Formalism: Joint Measurement for Heisenberg's Uncertainty Relation for Errors by Squeezed Coherent StatesWe point out that the Gaussian wave-packet formalism can serve as a concrete realization of the joint measurement of position and momentum, which is an essential element in understanding Heisenberg's original philosophy of the uncertainty principle, in line with the universal framework of error, disturbance, and their uncertainty relations developed by Lee and Tsutsui. We show that our joint measurement in the Gaussian phase space, being a Positive-Operator-Valued-Measure (POVM) measurement, smoothly interpolates between the projective measurements of position and momentum. We, for the first time, have obtained the Lee-Tsutsui (LT) error and the refined Lee error for the position-momentum measurement. We find that the LT uncertainty relation becomes trivial, 0 = 0, in the limiting case of projective measurement of either position or momentum. Remarkably, in contrast to the LT relation, the refined Lee uncertainty relation, which assesses errors for local representability, provides a constant lower bound unaffected by these limits and is invariably saturated, for a pure Gaussian initial state. The obtained lower bound is in agreement with Heisenberg's value.
ChatGPT-4o に考えてもらった宣伝文：
論文が出版されました。
ハイゼンベルクが最初に考えた、位置と運動量の同時測定についての基本的な問いに、
「やっぱり測定誤差ゼロにはならないよね」という決着をつけた内容です。
量子力学を勉強中の方にもおすすめです。
ぜひ読んでもらえたら嬉しいです。
arXiv.orgGaussian Formalism: Joint Measurement for Heisenberg's Uncertainty Relation for Errors by Squeezed Coherent StatesWe point out that the Gaussian wave-packet formalism can serve as a concrete realization of the joint measurement of position and momentum, which is an essential element in understanding Heisenberg's original philosophy of the uncertainty principle, in line with the universal framework of error, disturbance, and their uncertainty relations developed by Lee and Tsutsui. We show that our joint measurement in the Gaussian phase space, being a Positive-Operator-Valued-Measure (POVM) measurement, smoothly interpolates between the projective measurements of position and momentum. We, for the first time, have obtained the Lee-Tsutsui (LT) error and the refined Lee error for the position-momentum measurement. We find that the LT uncertainty relation becomes trivial, 0 = 0, in the limiting case of projective measurement of either position or momentum. Remarkably, in contrast to the LT relation, the refined Lee uncertainty relation, which assesses errors for local representability, provides a constant lower bound unaffected by these limits and is invariably saturated, for a pure Gaussian initial state. The obtained lower bound is in agreement with Heisenberg's value.