Quasi-hermitian Quantum Mechanics in Phase Space

We investigate quasi-hermitian quantum mechanics in phase space using standard deformation quantization methods: Groenewold star products and Wigner transforms. We focus on imaginary Liouville theory as a representative example where exact results are easily obtained. We emphasize spatially periodic solutions, compute various distribution functions and phase-space metrics, and explore the relationships between them.Comment: Accepted by Journal of Mathematical Physic

Logistic Map Potentials

We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x --> sx(1-x) for 0<s<=4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s>2. We illustrate the methods numerically for the cases s=5/2 and s=10/3

Compressed sensing quantum process tomography for superconducting quantum gates

We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an estimate for the process matrix $\chi$ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations. We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations we use two different bases in which the process matrix $\chi$ is approximately sparse, and show that the resulting estimates of the process matrices match each ther with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by not only its process matrix and fidelity, but also by the corresponding standard deviation, defined via variation of the state fidelity for different initial states.Comment: 16 pages, 11 figure

Local entanglement generation in the adiabatic regime

We study entanglement generation in a pair of qubits interacting with an initially correlated system. Using time independent perturbation theory and the adiabatic theorem, we show conditions under which the qubits become entangled as the joint system evolves into the ground state of the interacting theory. We then apply these results to the case of qubits interacting with a scalar quantum field. We study three different variations of this setup; a quantum field subject to Dirichlet boundary conditions, a quantum field interacting with a classical potential and a quantum field that starts in a thermal state.Comment: 9 pages, 6 figures. v2: reference [14] adde

Mutual Preservation of Entanglement

We study a generalized double Jaynes-Cummings (JC) model where two entangled pairs of two-level atoms interact indirectly. We focus on the case where the cavities and the entangled pairs are uncorrelated. We show that there exist initial states of the qubit system so that two entangled pairs are available at all times. In particular, the minimum entanglement in the pairs as a function of the initial state is studied. Finally, we extend our findings to a model consisting of multi-mode atom-cavity interactions. We use a non-Markovian quantum state diffusion (QSD) equation to obtain the steady-state density matrix for the qubits. We show that the multi-mode model also displays dynamical preservation of entanglement

Local Entanglement Generation in Two-Qubit Systems

We study the entanglement of two-qubit systems resulting from local interactions with spatially extended bosonic systems. Our results apply to the case where the initial state of the bosonic system is represented by a statistical mixture of states with fixed particle number. In particular, we derive and discuss necessary conditions to generate entanglement in the two-qubit system. We also study the scenario where the joint system is initially in its ground state and the interaction is switched on adiabatically. Using time independent perturbation theory and the adiabatic theorem, we show conditions under which the qubits become entangled as the joint system evolves into the ground state of the interacting theor

A chip-scale single-photon SWAP gate as integrated interface between polarization and spatial-momentum qubits

We demonstrate a single-photon SWAP gate between polarization and spatial momentum on a SOI chip. 19.8% error ratio is obtained, and phase coherence of the SWAP operation is measured via single photon interference with up to 58.7% visibility