Quantum State Tomography for Generic Pure States

TL;DR

This paper demonstrates that generic pure quantum states can be uniquely reconstructed from a minimal set of reduced density matrices, significantly reducing the number of measurements needed compared to previous methods.

Contribution

It introduces a new method to uniquely determine generic N-qudit pure states using only two specific reduced density matrices, reducing measurement complexity.

Findings

Unique determination of generic N-qudit pure states from two reduced density matrices

Reduction of measurement complexity from O(D log^2 D) to O(D)

Efficient reconstruction method for high-dimensional quantum states

Abstract

We show that a generic $N$-qudit pure quantum state is uniquely determined by only $2$ of its $\lceil\frac{N+1}{2}\rceil$-particle reduced density matrices. Therefore we give a method to uniquely determine a generic $N$-qudit pure state of dimension $D=d^N$ with $O(D)$ local measurements, which is an improvement comparing with the previous known approach using $O(D\log^2 D)$ or $O(D\log D)$ measurements.