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Frontiers in Optics

Polarization Characteristics of a Single Photon via Two Qubit Quantum State Tomography

Ali Akbar

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We demonstrate the Faraday rotation of single photon, generated from heralded down converted non-linear optical process. The state estimation is performed by two qubit quantum state tomography for temperature range 8–100 K and results are analyzed through minimization algorithms to extract Faraday rotation and ellipticity angles which are mapped on the Bloch sphere.

DOI
10.1364/fio.2022.jtu5b.13

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We demonstrate the Faraday rotation of single photon, generated from heralded down converted non-linear optical process. The state estimation is performed by two qubit quantum state tomography for temperature range 8–100 K and results are analyzed through minimization algorithms to extract Faraday rotation and ellipticity angles which are mapped on the Bloch sphere.
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∣Φ+⟩\vert \Phi^{+}\rangle∣Φ+⟩and∣Φ−⟩\left\vert\Phi^{-}\right\rangle∣Φ−⟩. 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.
We experimentally demonstrate a quantum state estimation and tomography for qubits encoded in a single photon's spatial degree of freedom. The experimental setup depicted in Fig. 1 consists of: 1) polarization entangled photon pairs source; 2) spatial encoder allowing to map a polarization state into spatial state; 3) polarization analyzer and 4) spatial state analyzer. The 28 element spatial quantum state measurement set was implemented using imaging optics and a linear array of 28 single photon avalanche diodes (SPAD). The timing information from all the detectors was acquired using custom made FPGA electronics.
Electron spins in semiconductor nanostructures are considered as one of the most promising candidates of the building blocks for quantum information processing. Initialization, coherent manipulation, and measurement of a single electron spin have been recently established. Here we explore the possibility to manipulate and measure by optical means the states of two electrons as a single qubit in nanostructures and propose methods of spin-state tomography based on Faraday or Kerr rotation for cases of both a single electron and two electrons, as well as a method of the Bell-state measurement for two electrons.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possibles paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possible paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.