Determining a quantum state by means of a single apparatus

TL;DR

This paper presents a method to determine an unknown quantum state using a single apparatus by interacting the system with a known auxiliary, enabling state reconstruction through measurements of a single observable.

Contribution

It introduces a one-to-one mapping between the quantum state and measurement probabilities using a single apparatus with a controlled interaction.

Findings

Single apparatus can determine quantum states via interaction with an auxiliary.

Simultaneous measurement of spins' z-components suffices after interaction.

Optimal setups involve Ising or anisotropic Heisenberg coupling with external fields.

Abstract

The unknown state $\hrho$ of a quantum system S is determined by letting it interact with an auxiliary system A, the initial state of which is known. A one-to-one mapping can thus be realized between the density matrix $\hrho$ and the probabilities of occurrence of the eigenvalues of a single and factorized observable of S+A, so that $\hrho$ can be determined by repeated measurements using a single apparatus. If S and A are spins, it suffices to measure simultaneously their $z$-components after a controlled interaction. The most robust setups are determined in this case, for an initially pure or a completely disordered state of A. They involve an Ising or anisotropic Heisenberg coupling and an external field.