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Quantum State Tomography of Single Qubit Using Density Matrix

Syafi’i Fahmi Bastian, Pruet Kalasuwan, Joko Purwanto

Published Feb 26, 2021• 0 citations
OpenAlex

Abstract

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%.

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arXiv:2503.07999•Mar 11, 2025•1 citation
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%.
The quantum state tomography is an essential component in the development of quantum technologies. It is a representation of polarization state which can be used to know the characterization of small particle called photon in the nanoscale. In this research, photon number has been measured in order to create the states tomography. Optical devices and quantum-mechanical approaches were used to accomplish the image of quantum state tomography. Due to a single qubit state density matrix can be represented by Stokes parameters, so there are four set-ups to measure the Stokes parameters for each sample. The density matrix in this work is used because the pure state only happen in theoretical idea. And in the real experiment, It always shows a mixed state. The density matrix will represent seven samples in this work. The samples of tomography measurements consist of horizontal state, vertical state, diagonal state, anti-diagonal state, right-circular state, left-circular state and the tomography of laser IR 808nm. In this work, state tomography is shown by 2x2 density matrix. This research also shows the fidelities between theory and experiment result. And it shows the good agreement. From this research, the state of laser beam has known. The laser that used is showing a vertical state with fidelity F=97,34%.
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.
Summary form only given. Full characterization of quantum states is increasingly important as ever more complex quantum systems are realized. Quantum state tomography of these systems is a difficult task because individual measurements only give partial information about the underlying density matrix of the system. Thus, conventionally the measurement apparatus must be reconfigured to take multiple measurements in order to fully determine the density matrix. It is accepted that for an W-qubit system an exponentially increasing number of measurements are needed [1]. As a consequence, the complexity of typical quantum state tomography grows exponentially with increasing photon number, which makes characterizing large quantum systems highly challenging. We formulate a concept of on-chip quantum tomography where the complexity scales linearly with the number of photons. This is achieved by using a single specially designed non-reconfigurable linear optical circuit as in Fig. 1(a). Crucially, the number of waveguides in this circuit scales linearly with the number of photons in the state to be measured. Furthermore, our approach is simple and robust, and we demonstrate it experimentally with a specially designed photonic chip.
We propose a technique for performing quantum state tomography of photonic polarization-encoded multiqubit states. Our method uses a single rotating wave plate, a polarizing beam splitter, and two photon-counting detectors per photon mode. As the wave plate rotates, the photon counters measure a pseudocontinuous signal which is then Fourier transformed. The density matrix of the state is reconstructed using the relationship between the Fourier coefficients of the signal and the Stokes' parameters that represent the state. The experimental complexity, i.e., different wave plate rotation frequencies, scales linearly with the number of qubits.
The reconstruction of density matrices from measurement data (quantum state tomography) is the most comprehensive method for assessing the accuracy and performance of quantum devices. Existing methods to reconstruct two-photon density matrices require the detection of both photons unless a priori information is available. Based on the concept of quantum-induced coherence by path identity, we present an approach to quantum state tomography that circumvents the requirement of detecting both photons. We show that an arbitrary two-qubit density matrix, which can contain up to fifteen free parameters, can be fully reconstructed from single-photon measurement data without any postselection and a priori information. In addition to advancing an alternative approach to quantum state measurement problems, our results also have notable practical implications. A practical challenge in quantum state measurement arises from the fact that effective single-photon detectors are not readily accessible for a wide spectral range. Our method, which eliminates the need for coincidence measurements, enables quantum state tomography in the case where one of the two photons is challenging or impossible to detect. It therefore opens the door to measuring quantum states hitherto inaccessible.