In order to solve the problem of information acquisition of quantum state,based on the quantum tomography theory,the single-qubit and multi-qubits tomography techniques are analyzed in details and an experiment for quantum state measurement is designed.Then the practicability of this method is verified by the simulation for single-qubit tomography with computer simulation technology.Simulation results show that not only the density matrix can be reconstructed and the information of quantum state can be obtained,but also the efficiency of experiment is satisfying,when suitable measurement times are chosen in quantum tomography experiment.
In order to solve the problem of information acquisition of quantum state,based on the quantum tomography theory,the single-qubit and multi-qubits tomography techniques are analyzed in details and an experiment for quantum state measurement is designed.Then the practicability of this method is verified by the simulation for single-qubit tomography with computer simulation technology.Simulation results show that not only the density matrix can be reconstructed and the information of quantum state can be obtained,but also the efficiency of experiment is satisfying,when suitable measurement times are chosen in quantum tomography experiment.
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields such as quantum computation, quantum communication, and quantum simulation. However, as the size of the quantum system increases, the number of measurement settings and sampling requirements for quantum state tomography grow exponentially with the number of qubits. This not only makes experimental design and implementation more complex, but also exacerbates the consumption of experimental resources. These limitations severely hinder the application of state tomography in large-scale quantum systems. To reduce measurement settings and improve sampling efficiency, this study proposes a state tomography method based on auxiliary systems. This method can be implemented through either entanglement between the quantum system to be measured and a quantum auxiliary system or through correlation between the quantum system and a probabilistic classical auxiliary system. Measurements on the entire joint system enable more efficient extraction of information about the quantum state to be measured. This method relies on standard quantum gate operations and requires only two measurement settings, with a total sampling complexity of O(d2), significantly simplifying experimental operations and measurement processes. Additionally, this study provides two schemes for measuring purity based on the proposed circuit, one of which achieves measurement precision at the Heisenberg limit. This study validates the effectiveness of the proposed method through a detailed theoretical analysis, a series of numerical simulations, and experiments.
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.
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 less 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 multi-qubit quantum states. Furthermore, this schema was proven to be robust through numerical simulations on a noisy superconducting qubit system. Therefore, the tomography schema paves an alternatively effective way to reconstruct the density matrix of a quantum state owing to its efficiency and accuracy, which are essential for quantum state tomography.
Abstract. The quantum state tomography is a fundamental part in the development of quantum technologies. It can be used to know the signal characterization of small particle called photon in the nanoscale. In this study, photon number has been measured in order to produce the states tomography. Optical devices and quantum-mechanical approaches were explored to obtain the quantum state tomography. Due to a single qubit state density matrix can be revealed by Stokes parameters, so there are four set-ups to measure the Stokes parameters for each sample. The density matrix is used because the pure state only appear theoreticaly. In the real experiment, It always exibits a mixed state. The samples of tomography measurements consist of linear state, cicular state and the IR 808nm. In this study, state tomography is shown by 2x2 density matrix. This experiment also provides the fidelities of experiment result. And it shows the good agreement. From this experiment, the state of IR 808nm has been detected. The laser that examined is showing a vertical state with fidelity F=97,34%.
A method of quantum-state tomography for quantum-information processing is described. The method is based on the use of the Fourier-transform technique and involves detection of all the diagonal elements of the density matrix in a one-dimensional experiment and all the off-diagonal elements by a two-dimensional experiment. The method is efficient for a large number of qubits (>5). The proposed method is outlined using a two-qubit system and demonstrated using simulations by tomographing arbitrary complex density matrices of two- and four-qubit systems.
Multi-qubit state tomography is a key problem in quantum information technology, which has been studied extensively. In this work, we focus on multi-qubit state tomography based on neural network estimators and typical conventional estimation approaches. For multi-qubit pure states, fully connected neural networks and restricted Boltzmann machine networks are designed, respectively, to carry out state tomography of 2-qubit (low-dimensional) systems and 5-qubit (high-dimensional) systems. Comparisons are made with maximum likelihood estimation and least squares estimation, where performance indicators are selected as reconstruction accuracy, time cost and the number of parameters. Simulation results indicate that intelligent approaches have significant advantages over conventional approaches for state tomography of low-dimensional systems; for high-dimensional systems, however, the conventional approach is still dominant when the measurement is complete, while the restricted Boltzmann machine network can achieve higher reconstruction accuracy when the measurement is incomplete.