Measuring complete quantum states with a single observable

TL;DR

This paper presents a method to determine an unknown quantum state using a single observable by coupling it to an assistant system, and demonstrates this experimentally with nuclear spins.

Contribution

It introduces a technique to measure complete quantum states from a single measurement by using an auxiliary system, advancing quantum state tomography methods.

Findings

Successful experimental implementation on nuclear spins.

Single observable measurement can fully determine quantum states.

Method reduces measurement complexity in quantum tomography.

Abstract

Experimental determination of an unknown quantum state usually requires several incompatible measurements. However, it is also possible to determine the full quantum state from a single, repeated measurement. For this purpose, the quantum system whose state is to be determined is first coupled to a second quantum system (the "assistant") in such a way that part of the information in the quantum state is transferred to the assistant. The actual measurement is then performed on the enlarged system including the original system and the assistant. We discuss in detail the requirements of this procedure and experimentally implement it on a simple quantum system consisting of nuclear spins.