Fourier State Tomography of Quantum Light

Quantum state tomography is used in quantum communication, computing, and cryptography to characterize quantum states enabling assessment and control of quantum systems. Rapidly scaling quantum technologies require fast, accurate, and simple techniques, but current tomography methods are bulky, hard to scale, and slow. To overcome these limitations, we experimentally demonstrate Fourier tomography [1], of single-photon and entangled photon pairs generated by a quantum dot. As shown in Fig. 1(a) for two-photon tomography, the setup consists of a continuously rotating quarter waveplate, a fixed linear polarizer and a single photon detector per qubit. As the waveplates rotates with different speed, we record the coincidences rate between the two detectors. This signal can be expressed as a Fourier series whose coefficients can be related to the polarization state of light. Fig. 1(b) shows the simulated coincidence rate as the waveplate rotates for input Bell states <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\vert \Phi^{+}\rangle$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\left\vert\Phi^{-}\right\rangle$</tex>. By capturing the coincidences variations as a Fourier series through a single rotating element and fixed polarizer, we simplify the tomography process, providing an accurate, and simple approach suitable for scalable quantum systems.