The concept of weak measurements and the super-efficiency of quantum tomography

TL;DR

This paper introduces quantum measurement protocols based on Lorentz transformations and weak perturbations, demonstrating super-efficient quantum tomography with higher fidelity than traditional POVM methods, especially effective for near-pure states.

Contribution

It proposes novel quantum measurement protocols utilizing Lorentz transformations that surpass traditional POVM methods in efficiency and fidelity, with potential for quantum system control.

Findings

Protocols can achieve higher fidelity than POVM measurements.

Weak perturbations enable effective quantum state control.

Super-efficiency is especially notable for near-pure states.

Abstract

The quantum measurement procedure based on the Lorentz transformation formalism and weak perturbation of the system is considered. In the simple case of a single-qubit it turns out that one can perform 4-dimension pseudo-rotation along with ordinary 3-dimension rotations on the Bloch sphere. These pseudo-rotations are similar to the Lorentz transformation in special relativity theory. The extension of the Lorentz transformation for many-qubit systems is also considered. The quantum measurement protocols based on the Lorentz transformation are proposed. It has been shown that these protocols cease to form the decomposition of unity and could be superefficient providing the fidelity higher than any POVM-measurement protocol. However, one can perform the complement of the Lorentz protocol to POVM-protocol by an additional measurement operator. If the initial mixed state is close to the pure one this operator corresponds to weak perturbation of the state while the original Lorentz protocol sets the strong perturbations. As the result, the feedback provides an effective control of a quantum system introducing weak perturbations to the quantum state. The results of this research are essential for the development of methods for the control of quantum information technologies.