Estimating the eigenstates of an unknown density operator without damaging it

TL;DR

This paper introduces a nondestructive measurement technique to estimate the eigenstates of an unknown density operator for qubits, using a radar-like scanning method on the Bloch sphere, revealing the mathematical structure of the Hilbert space.

Contribution

It presents a novel nondestructive measurement approach for eigenstate estimation that leverages projective measurements across all planes through the Bloch sphere center.

Findings

The method can approximately identify eigenstates without damaging the quantum system.

The approach demonstrates convergence, ensuring reliable eigenstate estimation.

It uncovers a mathematical structure of the n-fold Hilbert space related to the measurement process.

Abstract

Given n qubits prepared according to the same unknown density operator, we propose a nondestructive measuring method which approximately yields the eigenstates. It is shown that, for any plane which passes through the center point of the Bloch sphere, there exists corresponding projective measurement. By performing these measurements, we can scan the whole Bloch sphere like radar to search for the orientation of and determine the eigenstates. We show the convergency of the measurements. This result actually reveals a mathematical structure of the n-fold Hilbert space .