Cyclic measurements and simplified quantum state tomography

TL;DR

This paper introduces cyclic tight measurements that enable full quantum state tomography using only repeated applications of a single unitary device, simplifying experimental setups significantly.

Contribution

It proposes the concept of cyclic tight measurements and provides a practical method to implement them in any finite dimension, reducing experimental complexity.

Findings

Cyclic tight measurements enable efficient quantum state reconstruction.

The proposed setup simplifies experimental requirements for quantum tomography.

Validated the feasibility of cyclic measurements across finite dimensions.

Abstract

Tomographic reconstruction of quantum states plays a fundamental role in benchmarking quantum systems and accessing information encoded in quantum-mechanical systems. Among the informationally complete sets of quantum measurements, the tight ones provide a linear reconstruction formula and minimize the propagation of statistical errors. However, implementing tight measurements in the lab is challenging due to the high number of required measurement projections, involving a series of experimental setup preparations. In this work, we introduce the notion of cyclic tight measurements, which allow us to perform full quantum state tomography while considering only repeated application of a single unitary-based quantum device during the measurement stage. This type of measurement significantly simplifies the complexity of the experimental setup required to retrieve the quantum state of a physical system. Additionally, we design a feasible setup preparation procedure that produces well-approximated cyclic tight measurements in every finite dimension.