Exact Master Equation and Non-Markovian Decoherence for Quantum Dot Quantum Computing

In this article, we report the recent progress on decoherence dynamics of electrons in quantum dot quantum computing systems using the exact master equation we derived recently based on the Feynman-Vernon influence functional approach. The exact master equation is valid for general nanostructure systems coupled to multi-reservoirs with arbitrary spectral densities, temperatures and biases. We take the double quantum dot charge qubit system as a specific example, and discuss in details the decoherence dynamics of the charge qubit under coherence controls. The decoherence dynamics risen from the entanglement between the system and the environment is mainly non-Markovian. We further discuss the decoherence of the double-dot charge qubit induced by quantum point contact (QPC) measurement where the master equation is re-derived using the Keldysh non-equilibrium Green function technique due to the non-linear coupling between the charge qubit and the QPC. The non-Markovian decoherence dynamics in the measurement processes is extensively discussed as well.Comment: 15 pages, Invited article for the special issue "Quantum Decoherence and Entanglement" in Quantum Inf. Proces

Incomplete pure dephasing of N-qubit entangled W states

We consider qubits in a linear arrangement coupled to a bosonic field which acts as a quantum heat bath and causes decoherence. By taking the spatial separation of the qubits explicitly into account, the reduced qubit dynamics acquires an additional non-Markovian element. We investigate the time evolution of an entangled many-qubit W state, which for vanishing qubit separation remains robust under pure dephasing. For finite separation, by contrast, the dynamics is no longer decoherence-free. On the other hand, spatial noise correlations may prevent a complete dephasing. While a standard Bloch-Redfield master equation fails to describe this behavior even qualitatively, we propose instead a widely applicable causal master equation. Here we employ it to identify and characterize decoherence-poor subspaces. Consequences for quantum error correction are discussed.Comment: 14 pages, 6 figures, revised version, to appear in Phys. Rev.

Multipartite entanglement in the Fenna-Matthews-Olson (FMO) pigment-protein complex

We investigate multipartite states in the Fenna-Matthews-Olson (FMO) pigment-protein complex of the green sulfur bacteria using a Lorentzian spectral density of the phonon reservoir fitted with typical parameter estimates of the species, P. aestuarii. The evolution of the entanglement measure of the excitonic W qubit states is evaluated in the picosecond time range, showing increased revivals in the non-Markovian regime. Similar trends are observed in the evolution dynamics of the Meyer-Wallach measure of the N-exciton multipartite state, with results showing that multipartite entanglement can last from 0.5 to 1 ps, between the Bchls of the FMO complex. The teleportation and quantum information splitting fidelities associated with the GHZ and W_A resource states of the excitonic qubit channels of the FMO complex show that revivals in fidelities increase with the degree of non-Markovian strength of the decoherent environment. Results indicate that quantum information processing tasks involving teleportation followed by the decodification process involving W_A states of the FMO complex, may play a critical role during coherent oscillations at physiological temperatures.Comment: 16 pages, new figs, typo

Relations between entanglement and purity in non-Markovian dynamics

Knowledge of the relationships among different features of quantumness, like entanglement and state purity, is important from both fundamental and practical viewpoints. Yet, this issue remains little explored in dynamical contexts for open quantum systems. We address this problem by studying the dynamics of entanglement and purity for two-qubit systems using paradigmatic models of radiation-matter interaction, with a qubit being isolated from the environment (spectator configuration). We show the effects of the corresponding local quantum channels on an initial two-qubit pure entangled state in the concurrence-purity diagram and find the conditions which enable dynamical closed formulas of concurrence, used to quantify entanglement, as a function of purity. We finally discuss the usefulness of these relations in assessing entanglement and purity thresholds which allow noisy quantum teleportation. Our results provide new insights about how different properties of composite open quantum systems behave and relate each other during quantum evolutions.Comment: 16 Pages, 10 Figures. One author added. Improved version with more references and comment

Non-Markovian entanglement dynamics in coupled superconducting qubit systems

We theoretically analyze the entanglement generation and dynamics by coupled Josephson junction qubits. Considering a current-biased Josephson junction (CBJJ), we generate maximally entangled states. In particular, the entanglement dynamics is considered as a function of the decoherence parameters, such as the temperature, the ratio $r\equiv\omega_c/\omega_0$ between the reservoir cutoff frequency $\omega_c$ and the system oscillator frequency $\omega_0$, % between $\omega_0$ the characteristic frequency of the %quantum system of interest, and $\omega_c$ the cut-off frequency of %Ohmic reservoir and the energy levels split of the superconducting circuits in the non-Markovian master equation. We analyzed the entanglement sudden death (ESD) and entanglement sudden birth (ESB) by the non-Markovian master equation. Furthermore, we find that the larger the ratio $r$ and the thermal energy $k_BT$, the shorter the decoherence. In this superconducting qubit system we find that the entanglement can be controlled and the ESD time can be prolonged by adjusting the temperature and the superconducting phases $\Phi_k$ which split the energy levels.Comment: 13 pages, 3 figure

Moving Atom-Field Interactions: Quantum Motional Decoherence and Relaxation

The reduced dynamics of an atomic qubit coupled both to its own quantized center of mass motion through the spatial mode functions of the electromagnetic field, as well as the vacuum modes, is calculated in the influence functional formalism. The formalism chosen can describe the entangled non-Markovian evolution of the system with a full account of the coherent back-action of the environment on the qubit. We find a slight increase in the decoherence due to the quantized center of mass motion and give a condition on the mass and qubit resonant frequency for which the effect is important. In optically resonant alkali-metal atom systems, we find the effect to be negligibly small. The framework presented here can nevertheless be used for general considerations of the coherent evolution of qubits in moving atoms in an electromagnetic field.Comment: 9 pages, 1 figure, minor change