Direct Characteristic-Function Tomography of the Quantum States of Quantum Fields

Herein, we propose a novel strategy for implementing a direct readout of the symmetric characteristic function of the quantum states of quantum fields without the involvement of idealized measurements, an aspect that has always been deemed ill-defined in quantum field theory. This proposed scheme relies on the quantum control and measurements of an auxiliary qubit locally coupled to the quantum fields. By mapping the expectation values of both the real and imaginary parts of the field displacement operator to the qubit states, the qubit's readout provides complete information regarding the symmetric characteristic function. We characterize our technique by applying it to the Kubo-Martin-Schwinger (thermal) and squeezed states of a quantum scalar field. In addition, we have discussed general applications of this approach to analogue-gravity systems, such as Bose-Einstein condensates, within the scope of state-of-the-art experimental capabilities. This proposed strategy may serve as an essential in understanding and optimizing the control of quantum fields for relativistic quantum information applications, particularly in exploring the interplay between gravity and quantum, for example, the relation to locality, causality, and information.