Reconstruction of Liouvillian Superoperators

We show how to determine (reconstruct) a master equation governing the time evolution of an open quantum system. We present a general algorithm for the reconstruction of the corresponding Liouvillian superoperators. Dynamics of a two-level atom in various environments is discussed in detail.Comment: 4 pages, revtex, 1 eps figure, accepted for publication in Phys. Rev.

Distinguishing n Hamiltonians on C^n by a single measurement

If an experimentalist wants to decide which one of n possible Hamiltonians acting on an n dimensional Hilbert space is present, he can conjugate the time evolution by an appropriate sequence of known unitary transformations in such a way that the different Hamiltonians result in mutual orthogonal final states. We present a general scheme providing such a sequence.Comment: 4 pages, Revte

A Stochastic Liouville Equation Approach for the Effect of Noise in Quantum Computations

We propose a model based on a generalized effective Hamiltonian for studying the effect of noise in quantum computations. The system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. Treating these fluctuations as Gaussian Markov processes with zero mean and delta function correlation times, we derive an exact equation of motion describing the dissipative dynamics for a system of n qubits. We then apply this model to study the effect of noise on the quantum teleportation and a generic quantum controlled-NOT (CNOT) gate. For the quantum CNOT gate, we study the effect of noise on a set of one- and two-qubit quantum gates, and show that the results can be assembled together to investigate the quality of a quantum CNOT gate operation. We compute the averaged gate fidelity and gate purity for the quantum CNOT gate, and investigate phase, bit-flip, and flip-flop errors during the CNOT gate operation. The effects of direct inter-qubit coupling and fluctuations on the control fields are also studied. We discuss the limitations and possible extensions of this model. In sum, we demonstrate a simple model that enables us to investigate the effect of noise in arbitrary quantum circuits under realistic device conditions.Comment: 36 pages, 6 figures; to be submitted to Phys. Rev.

Vibrational pair cat states

Published versio

A Method for Modeling Decoherence on a Quantum Information Processor

We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an $N^2$-dimensional quantum environment and random classical fields. This model offers the advantage that it may be implemented on small quantum information processors in order to explore the intermediate regime between semiclassical and fully quantum models. We consider in particular $\sigma_z\sigma_z$ system-environment couplings which induce coherence (phase) damping, though the model is directly extendable to other coupling Hamiltonians. Effective, irreversible phase-damping of the system is obtained by applying an additional stochastic Hamiltonian on the environment alone, periodically redressing it and thereby irreversibliy randomizing the system phase information that has leaked into the environment as a result of the coupling. This model is exactly solvable in the case of phase-damping, and we use this solution to describe the model's behavior in some limiting cases. In the limit of small stochastic phase kicks the system's coherence decays exponentially at a rate which increases linearly with the kick frequency. In the case of strong kicks we observe an effective decoupling of the system from the environment. We present a detailed implementation of the method on an nuclear magnetic resonance quantum information processor.Comment: 12 pages, 9 figure

Quantum Logic Gates in Optical Lattices

We propose a new system for implementing quantum logic gates: neutral atoms trapped in a very far-off-resonance optical lattice. Pairs of atoms are made to occupy the same well by varying the polarization of the trapping lasers, and then a near-resonant electric dipole is induced by an auxiliary laser. A controlled-NOT can be implemented by conditioning the target atomic resonance on a resolvable level shift induced by the control atom. Atoms interact only during logical operations, thereby suppressing decoherence.Comment: Revised version, To appear in Phys. Rev. Lett. Three separate postscript figure

Generation of long-living entanglement using cold trapped ions with pair cat states

With the reliance in the processing of quantum information on a cold trapped ion, we analyze the entanglement entropy in the ion-field interaction with pair cat states. We investigate a long-living entanglement allowing the instantaneous position of the center-of-mass motion of the ion to be explicitly time dependent. An analytic solution for the system operators is obtained. We show that different nonclassical effects arise in the dynamics of the population inversion, depending on the initial states of the vibrational motion. We study in detail the entanglement degree and demonstrate how the input pair cat state is required for initiating the long living entanglement. This long living entanglement is damp out with an increase in the number difference $q$. Owing to the properties of entanglement measures, the results are checked using another entanglement measure (high order linear entropy).Comment: 15 pages, 7 figures, Sub. Appl. Phys. B: Laser and Optic

Trapped ions in the strong excitation regime: ion interferometry and non--classical states

The interaction of a trapped ion with a laser beam in the strong excitation regime is analyzed. In this regime, a variety of non--classical states of motion can be prepared either by using laser pulses of well defined area, or by an adiabatic passage scheme based on the variation of the laser frequency. We show how these states can be used to investigate fundamental properties of quantum mechanics. We also study possible applications of this system to build an ion interferometer.Comment: 9 pages, Revtex format, 5 compressed postscript figure

Experimental requirements for Grover's algorithm in optical quantum computation

The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a relatively simple implementation using only a single non-scalable CNOT gate to the most complex, requiring two concatenated scalable CNOT gates, and thus form a useful set of early milestones for LOQC. We also give a complete description of basic LOQC using polarization-encoded qubits, making use of many simplifications to the original scheme of Knill, Laflamme, and Milburn.Comment: 9 pages, 8 figure

Alluvial record of an early Eocene hyperthermal within the Castissent Formation, the Pyrenees, Spain

The late Palaeocene to the middle Eocene (57.5 to 46.5 Ma) recorded a total of 39 hyperthermals – periods of rapid global warming documented by prominent negative carbon isotope excursions (CIEs) as well as peaks in iron content – have been recognized in marine cores. Documenting how the Earth system responded to rapid climatic shifts during hyperthermals provides fundamental information to constrain climatic models. However, while hyperthermals have been well documented in the marine sedimentary record, only a few have been recognized and described in continental deposits, thereby limiting our ability to understand the effect and record of global warming on terrestrial systems. Hyperthermals in the continental record could be a powerful correlation tool to help connect marine and continental deposits, addressing issues of environmental signal propagation from land to sea. In this study, we generate new stable carbon isotope data (δ13C values) across the well-exposed and time-constrained fluvial sedimentary succession of the early Eocene Castissent Formation in the south central Pyrenees (Spain). The δ13C values of pedogenic carbonate reveal – similarly to the global records – stepped CIEs, culminating in a minimum δ13C value that we correlate with the hyperthermal event “U” at ca. 50 Ma. This general trend towards more negative values is most probably linked to higher primary productivity leading to an overall higher respiration of soil organic matter during these climatic events. The relative enrichment in immobile elements (Zr, Ti, Al) and higher estimates of mean annual precipitation together with the occurrence of small iron oxide and iron hydroxide nodules during the CIEs suggest intensification of chemical weathering and/or longer exposure of soils in a highly seasonal climate. The results show that even relatively small-scale hyperthermals compared with their prominent counterparts, such as PETM, ETM2, and ETM3, can leave a recognizable signature in the terrestrial stratigraphic record, providing insights into the dynamics of the carbon cycle in continental environments during these events