Quantum reciprocity relations for fluctuations of position and momentum

Pandit, Mahasweta ; Bera, Anindita ; Sen(De), Aditi ; Sen, Ujjwal (2019) Quantum reciprocity relations for fluctuations of position and momentum Physical Review A, 100 (1). ISSN 0031-899X (print); 1536-6065 (web)

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Official URL: https://doi.org/10.1103%2Fphysreva.100.012131

Abstract

We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is, in general, independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck's constant.

Item Type:Article
ID Code:125704
Deposited On:12 Oct 2022 09:18
Last Modified:12 Oct 2022 09:18

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