Tomography scheme for two spin-1/2 qubits in a double quantum dot

Abstract

We present a scheme for full quantum state tomography tailored for two spin qubits in a double quantum dot. A set of 15 quantum states allows to determine the density matrix in this two-qubit space by projective measurement. In this paper we choose a set gained from mutually unbiased bases. We determine how those 15 projections can be represented by charge measurements after a spin-to-charge conversion and the application of quantum gates. The quantum gates include exchange-based gates as well as rotations by electron spin resonance (ESR). We assume the experimental realization of ESR operations to be more difficult than the exchange gate operation. Therefore, it is an important result that the ESR gates are limited by a pi/2 rotation for one of the electron spins per measurement.

23 single-column pages, 2 figures

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• Preparation of quantum states of two spin-$\frac{1}{2}$ particles in the form of the Schmidt decomposition
• Optimal choice of state tomography quorum formed by projection operators
• Spectrum of Single-Photon Scattering in a Strong-Coupling Hybrid Optomechanical System
• Implementation of a two-qubit state by an auxiliary qubit on the three-spin system
• Quantum state tomography as a numerical optimization problem
• Enhanced Compressive Threshold Quantum State Tomography for Qudit Systems