Classical and Quantal State Reconstruction

TL;DR

This paper explores classical and quantum state reconstruction methods, emphasizing the role of mutual unbiased bases (MUB) for reconstructing states in finite-dimensional Hilbert spaces, providing a unified framework for both regimes.

Contribution

It introduces an alternative quantum state reconstruction method using MUB and applies it to finite-dimensional Hilbert spaces, clarifying the concept of MUB in quantum mechanics.

Findings

MUB are crucial for quantum state reconstruction.

The paper provides a detailed explanation of MUB in Hilbert spaces.

An alternative MUB-based reconstruction method is proposed.

Abstract

Analysis of state reconstruction both classical and quantum mechanical on equal footing is outlined. The meaning of "mutual unbiased bases" (MUB) of Hilbert spaces is explained in detail. An alternative quantum state reconstruction, that utilizes mutual unbiased bases (MUB), is given. The MUB approach is then used for state reconstruction in a finite, d, dimensional Hilbert spaces.