Tomographing Quantum State Tomography.

Muhammad Hamza Waseem, Faizan-e-Ilahi, Muhammad Sabieh Anwar

Rob Thew, Kae Nemoto, Andrew G. White +1 more

Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density matrix, relevant quantum information quantities such as the degree of entanglement and entropy can be calculated. Generally, orthogonal measurements have been discussed for this tomographic reconstruction. In this paper, we extend the tomographic reconstruction technique to two new regimes. First, we show how nonorthogonal measurements allow the reconstruction of the state of the system provided the measurements span the Hilbert space. We then detail how quantum-state tomography can be performed for multiqudits with a specific example illustrating how to achieve this in one- and two-qutrit systems.

Jochen Rau

I show that in tomographic experiments, the measurement of a small set of observables suffices to confirm or incrementally amend prior expectations with a high degree of confidence. To this end, I adapt the evidence procedure, an estimation technique used in classical image reconstruction, for use in quantum-state tomography.

M. Cramer, Martin Bodo Plenio, Steven T. Flammia +6 more

Xudan Chai, Teng Ma, Qihao Guo +3 more

In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, quantum state tomography, reconstructs the density matrix of an unknown quantum state. Theoretically, reconstructing an unknown state using this method can be arbitrarily accurate. However, this is not so practical owing to the huge burden of measurements and data processing for large numbers of qubits. Even comprising an efficient estimator and a precise algorithm, an optimal tomographic framework can also be overburdened owing to the exponential growth of the measurements. Moreover, the consequential postprocessing of huge amounts of data challenges the capacity of computers. Thus, it is crucial to build an efficient framework that requires fewer measurements but yields an expected accuracy. To this end, we built a tomography schema by which only a few Pauli measurements enable an accurate tomographic reconstruction. Subsequently, this schema was verified as efficient and accurate through numerical simulations on the tomography of multiqubit quantum states. Furthermore, it was proven to be robust through numerical simulations on a noisy superconducting qubit system. Therefore, the tomography schema paves an alternative effective way to reconstruct the density matrix of a quantum state owing to its efficiency and accuracy, which are essential for quantum state tomography.

Martin Ringbauer