State reconstruction of finite dimensional compound systems via local projective measurements and one-way classical communication

TL;DR

This paper presents a method for reconstructing the global state of finite-dimensional bipartite and multipartite quantum systems using only local projective measurements and one-way classical communication, simplifying the process.

Contribution

It establishes a direct relation between local projections and the global state, enabling state reconstruction with minimal measurement resources.

Findings

Reconstruction is possible with local projections and one-way communication.

The method applies to bipartite and multipartite systems.

Provides a practical approach for quantum state tomography.

Abstract

For a finite dimensional discrete bipartite system, we find the relation between local projections performed by Alice, and Bob post-selected state dependence on the global state submatrices. With this result the joint state reconstruction problem for a bipartite system can be solved with strict local projections and one-way classical communication. The generalization to multipartite systems is straightforward.