Quantum Tomography

This is the draft version of a review paper which is going to appear in "Advances in Imaging and Electron Physics"Comment: To appear in "Advances in Imaging and Electron Physics". Some figs with low resolutio

Super-Resolving Quantum Radar: Coherent-State Sources with Homodyne Detection Suffice to Beat the Diffraction Limit

There has been much recent interest in quantum metrology for applications to sub-Raleigh ranging and remote sensing such as in quantum radar. For quantum radar, atmospheric absorption and diffraction rapidly degrades any actively transmitted quantum states of light, such as N00N states, so that for this high-loss regime the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the linear Beer's law for classical radar attenuation, and which provide sensitivity at the shot-noise limit in the returned power. We show that coherent radar radiation sources, coupled with a quantum homodyne detection scheme, provide both longitudinal and angular super-resolution much below the Rayleigh diffraction limit, with sensitivity at shot-noise in terms of the detected photon power. Our approach provides a template for the development of a complete super-resolving quantum radar system with currently available technology.Comment: 23 pages, content is identical to published versio

Tomography of an optomechanical oscillator via parametrically amplified position measurement

We propose a protocol for quantum state tomography of nonclassical states in optomechanical systems. Using a parametric drive, the procedure overcomes the challenges of weak optomechanical coupling, poor detection efficiency, and thermal noise to enable high efficiency homodyne measurement. Our analysis is based on the analytic description of the generalized measurement that is performed when optomechanical position measurement competes with thermal noise and a parametric drive. The proposed experimental procedure is numerically simulated in realistic parameter regimes, which allows us to show that tomographic reconstruction of otherwise unverifiable nonclassical states is made possible.Comment: 37 pages, 5 figures, comments welcome. Published versio

Gaussian Quantum Information

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.Comment: 51 pages, 7 figures, submitted to Reviews of Modern Physic

Quantum Computed Green's Functions using a Cumulant Expansion of the Lanczos Method

In this paper, we present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical Mean Field Theory, and demonstrate the calculation of Green's functions on Quantinuum's H1-1 trapped-ion quantum computer. Our approach involves a cumulant expansion of the Lanczos method, using Hamiltonian moments as measurable expectation values. This bypasses the need for a large overhead in the number of measurements due to repeated applications of the variational quantum eigensolver (VQE), and instead measures the expectation value of the moments with one set of measurement circuits. From the measured moments, the tridiagonalised Hamiltonian matrix can be computed, which in turn yields the Green's function via continued fractions. While we use a variational algorithm to prepare the ground state in this work, we note that the modularity of our implementation allows for other (non-variational) approaches to be used for the ground state.Comment: 20 pages, 12 figure

On-chip generation and collectively coherent control of the superposition of the whole family of Dicke states

Integrated quantum photonics has recently emerged as a powerful platform for generating, manipulating, and detecting entangled photons. Multipartite entangled states lie at the heart of the quantum physics and are the key enabling resources for scalable quantum information processing. Dicke state is an important class of genuinely entangled state, which has been systematically studied in the light-matter interactions, quantum state engineering and quantum metrology. Here, by using a silicon photonic chip, we report the generation and collectively coherent control of the entire family of four-photon Dicke states, i.e. with arbitrary excitations. We generate four entangled photons from two microresonators and coherently control them in a linear-optic quantum circuit, in which the nonlinear and linear processing are achieved in a chip-scale device. The generated photons are in telecom band, which lays the groundwork for large-scale photonic quantum technologies for multiparty networking and metrology.Comment: 19 pages, 4 figures in the main text and 13 figures in the Supplemental Materia

Capacitive Memory Effect of Metal/Semiconductor Junction and Its Application in Superconducting Circuit QED

Department of PhysicsIn the superconducting quantum circuits, a LC oscillator is a main component and Josephson junction gives nonlinearity. Tuning of resonant frequency can be achieved in general by modulating a Josephson inductance of superconducting quantum interference device (SQUID) with magnetic flux. Here, it is proposed to realize tunable capacitor by using metal/semiconductor junction, which can be applied in the superconducting circuit system. Prior to realization of tunable capacitor, the electron transport at metal/semiconductor junctions is studied with two different interfacial layers, Al2O3 and graphene. The effects of interface states on electrical properties of the junction are studied by observing the change in Schottky barrier. First, the Schottky barrier height of Au/Ni/Al2O3/4H-SiC junction increases compared to that of Au/Ni/4H-SiC junction. It is because the electrostatic potential increases due to dipole effect on spontaneous polarization of 4H-SiC as a separation between metal and semiconductor increases. On the other hand, in case of Au/Graphene/4H-SiC junction, the Schottky barrier height decreases due to the presence of graphene. When the metal and graphene are in contact, there is charge transfer through Au/Graphene interface and then the graphene becomes doped. In addition, dipole is formed at the interface between Au and graphene. As a result, the effective work function becomes reduced, so does the Schottky barrier height. Based on the understanding of Schottky junction, tunable capacitor is realized by fabricating Au/Cr/Al2O3/Al/Si junction. With thick Al2O3 film, the electron transfer is blocked for the path between Cr and Al and is allowed only through the Al/Si Schottky junction. Then, the electrons can be captured in the Al floating metal. The amount of charge is dependent on the magnitude of voltage pulses and then discrete capacitance values can be defined. This capacitive memory effect of the tunable capacitor using Schottky junction is expected to be used in the superconducting quantum circuit system in respect that it can change the resonant frequency with discrete capacitance. Among the existing superconducting quantum circuit models, superconducting qubit is the most representative example of LC oscillators. Many superconducting circuit applications have been used to operate the qubits effectively. One promising application in the superconducting circuit QED is Josephson parametric amplifier (JPA). The JPA has been attracted as a device amplifying a signal in quantum-limited regime. It is observed in this dissertation that the JPA and Josephson parametric converter (JPC) which is another kind of JPA can improve the measurement efficiency in superconducting qubit detection. Also, the squeezed state which is another property of the JPA is studied by preparing it with the JPA and amplifying the squeezed signal with the JPC. The phase-dependence of the squeezed state is measured with homodyne setup and is reconstructed visually by using Wigner function. Finally, it is explored to reconstruct quantum state as a form of density matrix by using quantum state tomography (QST) in the superconducting multi-qubit system. It is important to extract quantum state in quantum information processing and necessary to expand the analysis on multi-qubit system. In this dissertation, the QSTs on two and three qubits are studied. A joint qubit readout method is used to measure an ensemble of the system. Also, Z-axis phase gate by using hyperbolic secant pulse is discussed in two qubit system. By using sech pulse, the phase accumulated during microwave-activated phase (MAP) gate can be controlled and eventually compensated. It is expected that the state fidelity can be improved by controlling phase on the qubit.clos