Pattern formation in quantum Turing machines

We investigate the iteration of a sequence of local and pair unitary transformations, which can be interpreted to result from a Turing-head (pseudo-spin $S$) rotating along a closed Turing-tape ($M$ additional pseudo-spins). The dynamical evolution of the Bloch-vector of $S$, which can be decomposed into $2^{M}$ primitive pure state Turing-head trajectories, gives rise to fascinating geometrical patterns reflecting the entanglement between head and tape. These machines thus provide intuitive examples for quantum parallelism and, at the same time, means for local testing of quantum network dynamics.Comment: Accepted for publication in Phys.Rev.A, 3 figures, REVTEX fil

Driven Spin Systems as Quantum Thermodynamic Machines: Fundamental Limits

We show that coupled two level systems like qubits studied in quantum information can be used as a thermodynamic machine. At least three qubits or spins are necessary and arranged in a chain. The system is interfaced between two split baths and the working spin in the middle is externally driven. The machine performs Carnot-type cycles and is able to work as heat pump or engine depending on the temperature difference of the baths $\Delta T$ and the energy differences in the spin system $\Delta E$. It can be shown that the efficiency is a function of $\Delta T$ and $\Delta E$.Comment: 9 pages, 11 figures, accepted for publication in Phys. Rev.

Multipartite entanglement in fermionic systems via a geometric measure

We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-1/2 fermions distributed over 2L modes (single particle states). The measure is defined on the 2L qubit space isomorphic to the Fock space for 2L single particle states. This entanglement measure is defined for a given partition of 2L modes containing m >= 2 subsets. Thus this measure applies to m <= 2L partite fermionic system where L is any finite number, giving the number of sites. The Hilbert spaces associated with these subsets may have different dimensions. Further, we have defined the local quantum operations with respect to a given partition of modes. This definition is generic and unifies different ways of dividing a fermionic system into subsystems. We have shown, using a representative case, that the geometric measure is invariant under local unitaries corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems. To the best of our knowledge, there is no usable entanglement measure of m > 3 partite fermionic systems in the literature, so that this is the first measure of multipartite entanglement for fermionic systems going beyond the bipartite and tripartite cases.Comment: 25 pages, 8 figure

Failure of Effective Potential Approach: Nucleus-Electron Entanglement in the He-Ion

Entanglement may be considered a resource for quantum-information processing, as the origin of robust and universal equilibrium behaviour, but also as a limit to the validity of an effective potential approach, in which the influence of certain interacting subsystems is treated as a potential. Here we show that a closed three particle (two protons, one electron) model of a He-ion featuring realistic size, interactions and energy scales of electron and nucleus, respectively, exhibits different types of dynamics depending on the initial state: For some cases the traditional approach, in which the nucleus only appears as the center of a Coulomb potential, is valid, in others this approach fails due to entanglement arising on a short time-scale. Eventually the system can even show signatures of thermodynamical behaviour, i.e. the electron may relax to a maximum local entropy state which is, to some extent, independent of the details of the initial state.Comment: Submitted to Europhysics Letter

Stability, Gain, and Robustness in Quantum Feedback Networks

This paper concerns the problem of stability for quantum feedback networks. We demonstrate in the context of quantum optics how stability of quantum feedback networks can be guaranteed using only simple gain inequalities for network components and algebraic relationships determined by the network. Quantum feedback networks are shown to be stable if the loop gain is less than one-this is an extension of the famous small gain theorem of classical control theory. We illustrate the simplicity and power of the small gain approach with applications to important problems of robust stability and robust stabilization.Comment: 16 page

Spectral densities and partition functions of modular quantum systems as derived from a central limit theorem

Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite number of subsystems. Even for only small numbers of subsystems we find good accordance with some known, exact results.Comment: 6 pages, 4 figures, some steps added to derivation, accepted for publication in J. Stat. Phy

On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering

We analyse the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the time parameter of a rather general class of stochastic filtering algorithms, including sequential Monte Carlo type models and mean eld particle interpretation models. We illustrate these results in the context of the Bernoulli and the Probability Hypothesis Density filter, yielding what seems to be the first results of this kind in this subject

Fluctuating work in coherent quantum systems: proposals and limitations

One of the most important goals in quantum thermodynamics is to demonstrate advantages of thermodynamic protocols over their classical counterparts. For that, it is necessary to (i) develop theoretical tools and experimental set-ups to deal with quantum coherence in thermodynamic contexts, and to (ii) elucidate which properties are genuinely quantum in a thermodynamic process. In this short review, we discuss proposals to define and measure work fluctuations that allow to capture quantum interference phenomena. We also discuss fundamental limitations arising due to measurement back-action, as well as connections between work distributions and quantum contextuality. We hope the different results summarised here motivate further research on the role of quantum phenomena in thermodynamics.Comment: As a chapter of: F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (eds.), "Thermodynamics in the quantum regime - Recent Progress and Outlook", (Springer International Publishing). Second version: Misspell in the title correcte

Work extremum principle: Structure and function of quantum heat engines

We consider a class of quantum heat engines consisting of two subsystems interacting via a unitary transformation and coupled to two separate baths at different temperatures $T_h > T_c$. The purpose of the engine is to extract work due to the temperature difference. Its dynamics is not restricted to the near equilibrium regime. The engine structure is determined by maximizing the extracted work under various constraints. When this maximization is carried out at finite power, the engine dynamics is described by well-defined temperatures and satisfies the local version of the second law. In addition, its efficiency is bounded from below by the Curzon-Ahlborn value $1-\sqrt{T_c/T_h}$ and from above by the Carnot value $1-(T_c/T_h)$. The latter is reached|at finite power|for a macroscopic engine, while the former is achieved in the equilibrium limit $T_h\to T_c$. When the work is maximized at a zero power, even a small (few-level) engine extracts work right at the Carnot efficiency.Comment: 16 pages, 5 figure

Dynamics of a Quantum Control-Not Gate for an Ensemble of Four-Spin Molecules at Room Temperature

We investigate numerically a single-pulse implementation of a quantum Control-Not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin ``molecules'' we simulate the time-evolution of the density matrix, for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of quantum CN gate in this system at finite temperature, using electromagnetic $\pi$-pulse.Comment: 7 pages 3 figure