Unitary Processes Research Articles

Unitary-process discrimination with error margin

We investigate a discrimination scheme between unitary processes. By introducing a margin for the probability of an erroneous guess, this scheme interpolates the two standard discrimination schemes: minimum-error and unambiguous discrimination. We present solutions for two cases. One is the case of two unitary processes with general prior probabilities. The other is the case with a group symmetry: The processes comprise a projective representation of a finite group. In the latter case, we found that unambiguous discrimination is a kind of ``all or nothing'': The maximum success probability is either 0 or 1. We also thoroughly analyze how entanglement with an auxiliary system improves discrimination performance.

Characterization of unitary processes with independent and stationary increments

Cet article poursuit la recherche initiée dans (Publ. Res. Inst. Math. Sci. 45 (2009) 745–785) pour caractériser les processus stationnaires unitaires gaussiens à incréments indépendants. L’hypothèse antérieure d’uniforme continuité est remplacée par de la continuité faible. Avec des conditions techniques sur le domaine du générateur, nous montrons que le processus est équivalent unitairement à la solution d’une équation de Hudson–Parthasarathy appropriée.

HIDDEN ENTANGLEMENT AND UNITARITY AT THE PLANCK SCALE

Attempts to go beyond the framework of local quantum field theory include scenarios in which the action of external symmetries on the quantum fields Hilbert space is deformed. We show how the Fock spaces of such theories exhibit a richer structure in their multi-particle sectors. When the deformation scale is proportional to the Planck energy, such new structure leads to the emergence of a "planckian" mode-entanglement, invisible to an observer that cannot probe the Planck scale. To the same observer, certain unitary processes would appear non-unitary. We show how entanglement transfer to the additional degrees of freedom can provide a potential way out of the black hole information paradox.

Single-shot discrimination of quantum unitary processes

We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination of unitary channels. We derive a ‘fidelity-like’ lower bound on the failure probability of the unambiguous discrimination of arbitrary quantum processes. This bound is saturated (in a certain range of a priori probabilities) in the case of unambiguous discrimination of unitary channels. Surprisingly, the optimal solution for both tasks is based on the optimization of the same quantity called completely bounded process fidelity.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

The central executive as a search process: Priming exploration and exploitation across domains.

The trade-off between exploration and exploitation is common to a wide variety of problems involving search in space and mind. The prevalence of this trade-off and its neurological underpinnings led us to propose domain-general cognitive search processes (Hills, Todd, & Goldstone, 2008). We propose further that these are consistent with the idea of a central executive search process that combines goal-handling across subgoal hierarchies. In the present study, we investigate 3 aspects of this proposal. First, the existence of a unitary central executive search process should allow priming from 1 search task to another and at multiple hierarchical levels. We confirm this by showing cross-domain priming from a spatial search task to 2 different cognitive levels within a lexical search task. Second, given the neural basis of the proposed generalized cognitive search process and the evidence that the central executive is primarily engaged during complex tasks, we hypothesize that priming should require search in the sense of a self-regulated making and testing of sequential predictions about the world. This was confirmed by showing that when participants were allowed to collect spatial resources without searching for them, no priming occurred. Finally, we provide a mechanism for the underlying search process and investigate 3 alternative hypotheses for subgoal hierarchies using the central executive as a search process model (CESP). CESP envisions the central executive as having both emergent and unitary processes, with one of its roles being a generalized cognitive search process that navigates goal hierarchies by mediating persistence on and switching between subgoals.

Unitary Processes with Independent Increments and Representations of Hilbert Tensor Algebras

The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson–Parthasarathy flow.

Experimental Quantum Process Discrimination

Discrimination between unknown processes chosen from a finite set is experimentally shown to be possible even in the case of nonorthogonal processes. We demonstrate unambiguous deterministic quantum process discrimination of nonorthogonal processes using properties of entanglement, additional known unitaries, or classical communication. Single qubit measurement and unitary processes and multipartite unitaries (where the unitary acts nonseparably across two distant locations) acting on photons are discriminated with a confidence of >or=97% in all cases.

Critically Damped Quantum Search

Although measurement and unitary processes can accomplish any quantum evolution in principle, thinking in terms of dissipation and damping can be powerful. We propose a modification of Grover's algorithm in which the idea of damping plays a natural role. Remarkably, we find that there is a critical damping value that divides between the quantum O(sqrt[N]) and classical O(N) search regimes. In addition, by allowing the damping to vary in a fashion we describe, one obtains a fixed-point quantum search algorithm in which ignorance of the number of targets increases the number of oracle queries only by a factor of 1.5.

Signatures of Incoherence in a Quantum Information Processor

Incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. While many incoherent processes appear decoherent, there are important differences. The distribution functions underlying incoherent processes are either static or slowly varying with respect to control operations and so the errors introduced by these distributions are refocusable. The observation and control of incoherence in small Hilbert spaces is well known. Here we explore incoherence during an entangling operation, such as is relevant in quantum information processing. As expected, it is more difficult to separate incoherence and decoherence over such processes. However, by studying the fidelity decay under a cyclic entangling map we are able to identify distinctive experimental signatures of incoherence. This is demonstrated both through numerical simulations and experimentally in a three qubit nuclear magnetic resonance implementation.

Subordination, Solidarity and the Limits of Popular Agency in a Yorkshire Valley c.1596-1615

Over the past decade, social historians of early modern England have found themselves drawn to the study of popular politics. Unlike earlier approaches to the subject, which tended to focus upon unitary processes of ‘politicization’, the new social history of politics has developed a broader sense of the political, centred upon power relations, agency and resistance.1 Most notably, this new social history of politics has questioned the validity of older approaches to the political, which tended to present early modern society as an organic hierarchy defined by popular deference and the uncritical acceptance of authority. Thus, Mark Kishlansky’s assumption that ‘in early modern England, political activity took place within the context of a hierarchical social structure and theocentric universe’, and that ‘social relations’ were conducted within ‘complex notions of honour, standing, and deference . . . [which] helped to regulate and absorb conflict between and within loosely defined status groups’ has in recent years been questioned. Whereas Kishlansky believed that early modern society was defined by ‘symbiotic relationships’, the new social historians of politics have emphasized the fluidity of power relations, the contingent nature of deference and the contested relationship between governor and governed.2

Incoherent noise and quantum information processing.

Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modeled as a distribution of unitary processes arising from slowly varying experimental parameters. We show how it introduces artifacts in quantum process tomography and we explain how the resulting estimate of the superoperator may not be completely positive. We then go on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of the superoperator eigenvalue spectra.

Application of a Single Model to Study the Adsorption Equilibrium of Prednisolone on Six Carbonaceous Materials

The knowledge of sorption processes of nonelectrolytes in solution by solid adsorbents implies the study of kinetics, equilibrium, and thermodynamic functions. However, quite frequently the equilibrium isotherms are studied by comparing them with those corresponding to the Giles et al. classification (1); these isotherms are also analyzed by fitting them to equations based on thermodynamic or kinetic criteria, and even to empirical equations. Nevertheless, information obtained is more coherent and satisfactory if the adsorption isotherms are fitted by using an equation describing the equilibrium isotherms according to the kinetic laws. These mentioned laws would determine each one of the unitary processes (one or more) which condition the global process. In this paper, an adsorption process of prednisolone in solution by six carbonaceous materials is explained according to a previously proposed single model, which allows to establish a kinetic law which fits satisfactorily most of C vs t isotherms (2). According to the above-mentioned kinetic law, equations describing sorption equilibrium processes have been deducted, and experimental data points have been fitted to these equations; such a fitting yields to different values of adsorption capacity and kinetic equilibrium constants for the different processes at several temperatures. However, in spite of their practical interest, these constants have no thermodynamic signification. Thus, the thermodynamic equilibrium constant (K) has been calculated by using a modified expression of the Gaines et al. equation (3). Global average values of the thermodynamic functions have also been calculated from the K values. Information related to variations of ΔH and ΔS with the surface coverage fraction was obtained by using the corresponding Clausius–Clapeyron equations.

Total internal reflection fluorescence microscopy for single-molecule imaging in living cells.

Marvelous background rejection in total internal reflection fluorescence microscopy (TIR-FM) has made it possible to visualize single-fluorophores in living cells. Cell signaling proteins including peptide hormones, membrane receptors, small G proteins, cytoplasmic kinases as well as small signaling compounds have been conjugated with single chemical fluorophore or tagged with green fluorescent proteins and visualized in living cells. In this review, the reasons why single-molecule analysis is essential for studies of intracellular protein systems such as cell signaling system are discussed, the instrumentation of TIR-FM for single-molecule imaging in living cells is explained, and how single molecule visualization has been used in cell biology is illustrated by way of two examples: signaling of epidermal growth factor in mammalian cells and chemotaxis of Dictyostelium amoeba along a cAMP gradient. Single-molecule analysis is an ideal method to quantify the parameters of reaction dynamics and kinetics of unitary processes within intracellular protein systems. Knowledge of these parameters is crucial for the understanding of the molecular mechanisms underlying intracellular events, thus single-molecule imaging in living cells will be one of the major technologies in cellular nanobiology.

Large Deviations Upper Bounds for the Laws of Matrix-Valued Processes and Non-Communicative Entropies

Using Itô’s calculus, we study the large deviations properties of the law of the spectral measure of the Hermitian Brownian motion.We extend this strategy to the symmetric, unitary and Wishart processes. This dynamical approach is generalized to the study of the large deviations of the non-commutative laws of several independent Hermitian Brownian motions. As a consequence, we can bound from above entropies defined in the spirit of the microstates entropy introduced by Voiculescu.

Lewis on Finkish Dispositions

Finkish dispositions, those dispositions that are lost when their conditions of realization occur, pose deep problems for counterfactual accounts of dispositions. David Lewis has argued that the counterfactual approach can be rescued, offering such an account that purports to handle finkish as well as other dispositions. The paper argues that Lewis's account fails to account for several kinds of dispositions, one of which involves failure to distinguish parallel processes from unitary processes.

Unitary orthogonalization processes

All methods for solving least-squares problems involve orthogonalization in one way or another. Certain fundamental estimation and prediction problems of signal processing and time-series analysis can be formulated as least-squares problems. In these problems, the sequence that is to be orthogonalized is generated by an underlying unitary operator. A prime example of an efficient orthogonalization procedure for this class of problems is Gragg's isometric Arnoldi process, which is the abstract encapsulation of a number of concrete algorithms. In this paper, we discuss a two-sided orthogonalization process that is equivalent to Gragg's process but has certain conceptual strengths that warrant its introduction. The connections with classical algorithms of signal processing are discussed.

Stepanov Almost Periodically Correlated and Almost Periodically Unitary Processes

This paper extends the structure and properties of almost periodically correlated (APC) and almost periodically unitary (APU) processes, which were defined in the sense of Bohr, to a larger class of processes for which the sense of almost periodicity is that of Stepanov. These processes are not necessarily continuous in quadratic mean, as are the Bohr APC and APU processes, yet exhibit a sense of almost periodicity. For example, processes formed by amplitude modulation $f(t)\,X(t)$ or time-scale modulation $X(t+f(t))$ of a wide sense stationary process $X(t)$ by a scalar Stepanov AP function $f(t)$, which need not be continuous, are Stepanov APU and APC. The principal results on APC and APU processes are extended to the new class. We extend Gladyshev's characterization of APC correlation functions to Stepanov APC processes and show that their correlation functions are completely represented by a Fourier series having a countable number of coefficient functions that are Fourier transforms of complex measures. We show that Stepanov APU processes are also Stepanov APC and are given by $X(t)=U(t)\,[P(t)]$, where $\{U(t),\ t\in\bR\}$ is a strongly continuous group of unitary operators and $P(t)$ is a vector-valued Stepanov almost periodic function. As in the case of Bohr APU processes, the preceding fact leads to representations of $X(t)$ based on the spectral theory for unitary operators and for Stepanov almost periodic functions.

Stepanov almost periodically correlated and almost periodically unitary processes

Stepanov almost periodically correlated and almost periodically unitary processes

Physical aspect of the improvement of quantum-noise characteristics caused by unitary transformation with a nonlinear optical medium.

The standard quantum limit (SQL) as an error probability can be broken by means of a unitary transformation such as a Kerr medium installed before the conventional homodyne scheme. Such an improvement in the error probability cannot be realized by the conventional unitary transformer like squeezers for fixed coherent state inputs. The physical origin of this effect is nonlinear quantum interference for the components of the output state evolved from the input coherent state. We clarify the conditions for overcoming the SQL by unitary transformation and show several examples of the interaction Hamiltonian which generate unitary processes to break the SQL.