Speaker
Ujjwal Sen
Description
Ujjwal Sen
Quantum uncertainty relations: some further landscapes
We wish to discuss about two related topics.
Based on the statistical concept of the median, we will propose a quantum uncertainty relation between spreads of the position and momentum distributions of arbitrary quantum states. The relation will be universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We will show that the median-based one is not saturated for Gaussian distributions in position.
In the second part, we will propose a quantum uncertainty relation for arbitrary quantum states in terms of Lipschitz constants of the corresponding position and momentum probability distributions. 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. We find that the product of the Lipschitz constants is greater than the inverse square of the Planck constant.
Quantum uncertainty relations: some further landscapes
We wish to discuss about two related topics.
Based on the statistical concept of the median, we will propose a quantum uncertainty relation between spreads of the position and momentum distributions of arbitrary quantum states. The relation will be universal, unlike that based on the mean and standard deviation, as the latter may become non-existent or ineffective in certain cases. We will show that the median-based one is not saturated for Gaussian distributions in position.
In the second part, we will propose a quantum uncertainty relation for arbitrary quantum states in terms of Lipschitz constants of the corresponding position and momentum probability distributions. 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. We find that the product of the Lipschitz constants is greater than the inverse square of the Planck constant.
Primary author
Prof.
Ujjwal Sen
