Self-calibrating Quantum State Tomography

TL;DR

This paper presents a novel self-calibrating quantum state tomography method that accurately reconstructs multi-qubit states despite unknown measurement basis rotations, demonstrated on photon states with practical, low-cost hardware.

Contribution

The authors introduce a self-calibrating tomography technique capable of reconstructing quantum states with unknown measurement rotations, including the magnitude of these rotations, using inexpensive hardware.

Findings

Achieved high-fidelity state reconstruction on photon states

Demonstrated the method with low-cost birefringent polymer and liquid crystal devices

Potential applications in biological systems with unknown transition dipoles

Abstract

We introduce and experimentally demonstrate a technique for performing quantum state tomography on multiple-qubit states despite incomplete knowledge about the unitary operations used to change the measurement basis. Given unitary operations with unknown rotation angles, our method can be used to reconstruct the density matrix of the state up to local sigma-z rotations as well as recover the magnitude of the unknown rotation angle. We demonstrate high-fidelity self-calibrating tomography on polarization-encoded one- and two-photon states. The unknown unitary operations are realized in two ways: using a birefringent polymer sheet---an inexpensive smartphone screen protector---or alternatively a liquid crystal wave plate with a tuneable retardance. We explore how our technique may be adapted for quantum state tomography of systems such as biological molecules where the magnitude and orientation of the transition dipole moment is not known with high accuracy.