High-fidelity tracking of the evolution of multilevel quantum states

TL;DR

This paper introduces a high-precision quantum tomography method for tracking multilevel quantum states using novel algorithms based on Lorentz transformations, enabling superior control and measurement accuracy in quantum systems.

Contribution

It presents new algorithms for quantum control utilizing Lorentz transformations, enhancing the precision of quantum state evolution tracking and control.

Findings

High-accuracy quantum tomography for multilevel systems.

Feedback control via weak measurements achieves superior precision.

Algorithms outperform standard POVM protocols in measurement accuracy.

Abstract

The method of quantum tomography, which allows us to track with high accuracy the evolution of multilevel quantum systems (qudits) in Hilbert spaces of various dimensions is presented. The developed algorithms for quantum control are based on the use of the spinor representation of the Lorentz transformation group. In the simplest case of one-qubit states, it turns out that, in addition to three-dimensional rotations on the Bloch sphere, one can introduce four-dimensional Lorentz pseudorotations, similar to the transformations of the special theory of relativity. We show that feedback through weakly perturbing adaptive quantum measurements turns out to be capable of providing high-precision control of the quantum system, while introducing only weak perturbations into the initial quantum state. It turns out that, together with the control of a quantum system through its weak perturbation, the developed algorithms for controlling the evolution of the state of a quantum system can be super-efficient, providing a higher measurement accuracy than any standard POVM (Positive-Operator Valued Measure) protocols. The results of the study are important for the development of optimal adaptive methods for quantum states and operations controlling. The results obtained are essential for the development of high-precision control methods for quantum information technologies.