Method for the Quantum Metric Tensor Measurement in a Continuous Variable System

Abstract

As a fundamental concept, geometry is widely used in understanding physical phenomena. In quantum mechanics, geometry is related to the system’s quantum state and can be characterized by the quantum geometric tensor (QGT), whose real part is referred to as the quantum metric tensor (QMT), which defines the distance between two neighboring quantum states in the projected Hilbert space. Several pieces of research based on discrete variables have been proposed to extract the QMT, but research with the use of continuous variables is lacking. Here, we propose a method to extract the QMT of a continuous variable system, specified here as a cat-qubit. The method is developed by constructing the Kerr nonlinear parametric oscillator (KNPO) and by modulating it with external drives to induce adiabatic dynamics process within the state subspace spanned by the even and odd Scho¨dinger cat states. The method paves the way for exploring the geometry for continuous variable systems.