The purpose of this monograph is to show how different discrete variables of light can be used to generate qubits. In particular, the tomographic preparation and reconstruction process for the polarization and path variables in photons is shown. In addition, the preparation of two-qubit states in a single photon using these variables is done, and these states are used to generate statistical mixtures states on the path. Finally, an experimental setup is proposed for the reconstruction of two-qubit states in a single photon. During the monograph, two different tomography techniques are used: Standard quantum state tomography and quantum state tomography through the use of mutually unbiased basesThe purpose of this monograph is to show how different discrete variables of light can be used to generate qubits. In particular, the tomographic preparation and reconstruction process for the polarization and path variables in photons is shown. In addition, the preparation of two-qubit states in a single photon using these variables is done, and these states are used to generate statistical mixtures states on the path. Finally, an experimental setup is proposed for the reconstruction of two-qubit states in a single photon. During the monograph, two different tomography techniques are used: Standard quantum state tomography and quantum state tomography through the use of mutually unbiased bases

Jan 1, 20180 citations

Quantum tomography of time-delocalized single photons

Zavatta A., E. M. D'Angelo, Valentina Parigi +1 more

Jan 1, 20060 citations

Quantum tomography for solid state qubits

Yu-xi Liu, L. F. Wei, Franco Nori

PACS. 03.65.Ta – Foundations of quantum mechanics; measurement theory. PACS. 03.65.Wj – State reconstruction, quantum tomography. Abstract. – We propose a method for the tomographic reconstruction of qubit states for a general class of solid-state systems in which the Hamiltonians are represented by spin operators, e.g., with Heisenberg-, XXZ-, or XY-type exchange interactions. We analyze the implementation of the projective operator measurements, or spin measurements, on qubit states. All the qubit states for the spin Hamiltonians can be reconstructed by using experimental data. Quantum information processing requires the effective measurement of quantum states. However, a single quantum measurement can only obtain partial information of a quantum state. The reconstruction of a quantum state requires measuring a complete set of observables on an ensemble of identically prepared copies of the system. This method called quantum state tomography [1], is very important because any unknown state can be ascertained by tomographic measurements. Moreover, the full description of qubit states can increase the accuracy of quantum operations. Tomographic measurements have been experimentally implemented for, e.g., the nuclear spin state of an NMR system [2], the electromagnetic field and photonPACS. 03.65.Ta – Foundations of quantum mechanics; measurement theory. PACS. 03.65.Wj – State reconstruction, quantum tomography. Abstract. – We propose a method for the tomographic reconstruction of qubit states for a general class of solid-state systems in which the Hamiltonians are represented by spin operators, e.g., with Heisenberg-, XXZ-, or XY-type exchange interactions. We analyze the implementation of the projective operator measurements, or spin measurements, on qubit states. All the qubit states for the spin Hamiltonians can be reconstructed by using experimental data. Quantum information processing requires the effective measurement of quantum states. However, a single quantum measurement can only obtain partial information of a quantum state. The reconstruction of a quantum state requires measuring a complete set of observables on an ensemble of identically prepared copies of the system. This method called quantum state tomography [1], is very important because any unknown state can be ascertained by tomographic measurements. Moreover, the full description of qubit states can increase the accuracy of quantum operations. Tomographic measurements have been experimentally implemented for, e.g., the nuclear spin state of an NMR system [2], the electromagnetic field and photon

Jan 1, 200419 citations

Tomographic reconstruction of the single-photon Fock state by high-frequency homodyne detection

Alessandro Zavatta, Silvia Viciani, Marco Bellini

A single-photon Fock state has been generated by means of conditional preparation from a two-photon state emitted in the process of spontaneous parametric down-conversion. A recently developed high-frequency homodyne tomography technique has been used to completely characterize the Fock state by means of a pulse-to-pulse analysis of the detectors' difference photocurrent. The density matrix elements of the generated state have been retrieved with a final detection efficiency of about 57%. A comparison has been performed between the phase-averaged tomographic reconstructions of the Wigner function as obtained from the measured density-matrix elements and from a direct Abel transform of the homodyne data. The ability of our system to work at the full repetition rate of the pulsed laser $(82\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})$ substantially simplifies the detection scheme, allowing for more ``exotic'' quantum states to be generated and analyzed.A single-photon Fock state has been generated by means of conditional preparation from a two-photon state emitted in the process of spontaneous parametric down-conversion. A recently developed high-frequency homodyne tomography technique has been used to completely characterize the Fock state by means of a pulse-to-pulse analysis of the detectors' difference photocurrent. The density matrix elements of the generated state have been retrieved with a final detection efficiency of about 57%. A comparison has been performed between the phase-averaged tomographic reconstructions of the Wigner function as obtained from the measured density-matrix elements and from a direct Abel transform of the homodyne data. The ability of our system to work at the full repetition rate of the pulsed laser $(82\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})$ substantially simplifies the detection scheme, allowing for more ``exotic'' quantum states to be generated and analyzed.

arXiv:quant-ph/0406090Physical Review ANov 23, 2004133 citations

Quantum tomography of three-qubit state

Naser Karimi, Marziyeh Yahyavi

Optics CommunicationsFeb 17, 20251 citation

(82\phantom{\rule{0.3em}{0ex}}\mathrm{MHz})

substantially simplifies the detection scheme, allowing for more ``exotic'' quantum states to be generated and analyzed.