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arXiv:2101.00016 · Acta Physica Polonica A

Quantum State Tomography of Four-Level Systems with Noisy Measurements

Artur Czerwiński

Published Jun 1, 2021• 5 citations
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Abstract

In this article, we investigate the problem of state reconstruction of four-level quantum systems.A realistic scenario is considered with measurement results distorted by random unitary operators.Two frames that define injective measurements are applied and compared.By introducing arbitrary rotations, we can test the performance of the framework versus the amount of experimental noise.The results of numerical simulations are depicted in graphs and discussed.In particular, a class of entangled states is reconstructed.The concurrence is used as a figure of merit to quantify how well entanglement is preserved through noisy measurements.

DOI
10.12693/aphyspola.139.666

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In this article, we investigate the problem of state reconstruction of four-level quantum systems.A realistic scenario is considered with measurement results distorted by random unitary operators.Two frames that define injective measurements are applied and compared.By introducing arbitrary rotations, we can test the performance of the framework versus the amount of experimental noise.The results of numerical simulations are depicted in graphs and discussed.In particular, a class of entangled states is reconstructed.The concurrence is used as a figure of merit to quantify how well entanglement is preserved through noisy measurements.
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Abstract Quantum state tomography (QST) represents an essential tool for the characterization, verification, and validation (QCVV) of quantum processors. Only for a few idealized scenarios, there are analytic results for the optimal measurement set for QST. E.g., in a setting of non-degenerate measurements, an optimal minimal set of measurement operators for QST has eigenbases which are mutually unbiased. However, in other set-ups, dependent on the rank of the projection operators and the size of the quantum system, the optimal choice of measurements for efficient QST needs to be numerically approximated. We have generalized this problem by introducing the framework of customized efficient QST. Here we extend customized QST and look for the optimal measurement set for QST in the case where some of the quantum gates applied in the measurement process are noisy. To achieve this, we use two distinct noise models: first, the depolarizing channel, and second, over- and under-rotation in single-qubit and to two-qubit gates (for further information, please see Methods). We demonstrate the benefit of using entangling gates for the efficient QST measurement schemes for two qubits at realistic noise levels, by comparing the fidelity of reconstruction of our optimized QST measurement set to the state-of-the-art scheme using only product bases.
The article undertakes the problem of pure state estimation from projective measurements based on photon counting.Two generic frames for qubit tomography are considered -one composed of the elements of the SIC-POVM and the other defined by the vectors from the mutually unbiased bases.Both frames are combined with the method of least squares in order to reconstruct a sample of input qubits with imperfect measurements.The accuracy of each frame is quantified by the average fidelity and purity.The efficiency of the frames is compared and discussed.The method can be generalized to higher-dimensional states and transferred to other fields where the problem of complex vectors reconstruction appears.
We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the fundamental limit. In the present work the notions of ideal and non-ideal quantum measurements are strictly formalized. It is shown that non-ideal quantum measurements could be represented as a mixture of ideal measurements. Based on root approach the quantum state reconstruction method is developed. Informational accuracy theory of non-ideal quantum measurements is proposed. The monitoring of the amount of information about the quantum state parameters is examined, including the analysis of the information degradation under the noise influence. The study of achievable fidelity in non-ideal quantum measurements is performed. The results of simulation of fidelity characteristics of a wide class of quantum protocols based on polyhedrons geometry with high level of symmetry are presented. The impact of different decoherence mechanisms, including qubit amplitude and phase relaxation, bit-flip and phase-flip, is considered.
In this article, we introduce a framework for two-qutrit Werner states tomography with Gaussian noise. The measurement scheme is based on the symmetric, informationally complete positive operator-valued measure. To make the framework realistic, we impose the Gaussian noise on the measured states numbers. Through numerical simulation, we successfully reconstructed the two-qutrit Werner states in various experimental scenarios and analyzed the optimal scenario from four aspects: fidelity, purity, entanglement, and coherence.
In this article, we introduce a framework for quantum state tomography of qutrits by projective measurements.The framework is based on photon-counting with measurement results distorted due to the Poisson noise and dark counts.Two different measurement schemes are investigated numerically and compared in terms of their efficiency for distinct numbers of photons per measurement.The accuracy of state reconstruction is quantified by figures of merit which are presented on graphs versus the amount of noise.