Showing papers on "Unitary state published in 2006"

Hudson's theorem for finite-dimensional quantum systems

Abstract: We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson’s theorem. Hudson established that for continuous variable systems, the Wigner function of a pure state has no negative values if and only if the state is Gaussian. Turning to mixed states, it might be surmised that only convex combinations of stabilizer states give rise to non-negative Wigner distributions. We refute this conjecture by means of a counterexample. Further, we give an axiomatic characterization which completely fixes the definition of the Wigner function and compare two approaches to stabilizer states for Hilbert spaces of prime-power dimensions. In the course of the discussion, we derive explicit formulas for the number of stabilizer codes defined on such systems.

New perspectives on unitary coupled-cluster theory

Abstract: The advantages and possibilities of a unitary coupled-cluster (CC) theory are examined. It is shown that using a unitary parameterization of the wave function guarantees agreement between a sum-over-states polarization propagator and response theory calculation of properties of arbitrary order, as opposed to the case in conventional CC theory. Then, using the Zassenhaus expansion for noncommuting exponential operators, explicit diagrams for an extensive and variational method based on unitary CC theory are derived. Possible extensions to the approximations developed are discussed as well. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Collective and unitary models: A clarification

Abstract: In this note we identify and clarify a confusion that has arisen in the literature about the exact relationship between unitary and collective models and what enters the Pareto weight and the sharing function. We suggest that we should denote as ‘unitary’ any model that leads to outcomes that satisfy the Slutsky conditions whether or not these outcomes depend on distribution factors. In particular, income pooling is neither necessary nor sufficient for a unitary model. We also show that the presence of prices or total expenditure in the sharing rule cannot be used as a test for a unitary model.

The Information-Disturbance Tradeoff and the Continuity of Stinespring's Representation

Abstract: Stinespring's dilation theorem is the basic structure theorem for quantum channels: it states that any quantum channel arises from a unitary evolution on a larger system. Here we prove a continuity theorem for Stinespring's dilation: if two quantum channels are close in cb-norm, then it is always possible to find unitary implementations which are close in operator norm, with dimension-independent bounds. This result generalizes Uhlmann's theorem from states to channels and allows to derive a formulation of the information-disturbance tradeoff in terms of quantum channels, as well as a continuity estimate for the no-broadcasting theorem. We briefly discuss further implications for quantum cryptography, thermalization processes, and the black hole information loss puzzle.

On SIC-POVMs in prime dimensions

Abstract: The generalized Pauli group and its normalizer, the Clifford group, have a rich mathematical structure which is relevant to the problem of constructing symmetric informationally complete POVMs (SIC-POVMs). To date, almost every known SIC-POVM fiducial vector is an eigenstate of a 'canonical' unitary in the Clifford group. I show that every canonical unitary in prime dimensions p > 3 lies in the same conjugacy class of the Clifford group and give a class representative for all such dimensions. It follows that if even one such SIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them are (for a given such dimension). I also conjecture that in all dimensions d, the number of conjugacy classes is bounded above by 3 and depends only on dmod9, and I support this claim with computer computations in all dimensions <48.

Unitary Shimura correspondences for split real groups

Abstract: We find a relationship between certain complementary series representations for nonlinear coverings of split simple groups, and spherical complementary series for (different) linear groups. The main technique is Barbasch's method of calculating some intertwining operators purely in terms of the Weyl group

On SIC-POVMs in Prime Dimensions

Abstract: The generalized Pauli group and its normalizer, the Clifford group, have a rich mathematical structure which is relevant to the problem of constructing symmetric informationally complete POVMs (SIC-POVMs). To date, almost every known SIC-POVM fiducial vector is an eigenstate of a "canonical" unitary in the Clifford group. I show that every canonical unitary in prime dimensions p > 3 lies in the same conjugacy class of the Clifford group and give a class representative for all such dimensions. It follows that if even one such SIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them are (for a given such dimension). I also conjecture that in all dimensions d, the number of conjugacy classes is bounded above by 3 and depends only on d mod 9, and I support this claim with computer computations in all dimensions < 48.

Unambiguous pure-state identification without classical knowledge

Abstract: We study how to unambiguously identify a given quantum pure state with one of the two reference pure states when no classical knowledge on the reference states is given but a certain number of copies of each reference quantum state are presented. By unambiguous identification, we mean that we are not allowed to make a mistake but our measurement can produce an inconclusive result. Assuming the two reference states are independently distributed over the whole pure state space in a unitary invariant way, we determine the optimal mean success probability for an arbitrary number of copies of the reference states and a general dimension of the state space. It is explicitly shown that the obtained optimal mean success probability asymptotically approaches that of the unambiguous discrimination as the number of the copies of the reference states increases.

Devolution in the United Kingdom: Statehood and Citizenship in Transition

Abstract: The United Kingdom evolved as a "state of unions," in which government arrangements were territorially varied in line with the particular circumstances of the sequence of acts of union between the core state territory of England and Wales, Scotland, and Ireland. The recent devolution reforms have built on that territorial nonuniformity, embedding a number of idiosyncrasies into the devolved UK state: a lopsidedness that leaves the biggest and wealthiest part of the United Kingdom?England?governed centrally wihle the non English nations have devolved government, devolved government arrangements for those nations that are markedly asymmetrical, and an underdeveloped system of intergovern mental relations connecting United Kingdom?level and devolved political arenas. Together these issues pose important questions of whether the devolution reforms amount to a coherent overall package, whether the reforms are stable, and whether they erode a common UK citizenship. The United Kingdom has a reputation as one of the more centralized states in contemporary Europe. In that light the devolution reforms introduced by the United Kingdom's Labour governments since 1997?the Scottish parliament, the National Assembly for Wales and the Northern Ireland Assembly?appear to be a radical break. Some of that appearance is misleading. Devolution, in fact, was a deceptively simple thing to do. To understand why, the dominant conceptualization of the United Kingdom as a unitary state must be challenged. The United Kingdom is in many respects a highly centralized political system, with power formally concentrated in a famously?or notoriously?strong and putatively sovereign parliament. But this centralized power was never effectively used to create a territorially uniform state. The devolution reforms have built on that residual territorial nonuniformity. In effect they have done little more than to democratize the distinctive administrative arrangements that had emerged over centuries for delivering UK policies outside the core state

Evaluating the Move to a Linear Tax System in Germany and Other European Countries

Abstract: This paper proposes a comparison of the results of tax policy analysis obtained on the basis of unitary and collective representations of the household. We first generate labour supplies consistent with the collective rationality, by use of a model calibrated on microdata as described in Vermeulen et al. [Collective Models of Household Labor Supply with Nonconvex Budget Sets and Nonparticipation: A Calibration Approach (2006)]. A unitary model is then estimated on these collective data and unitary and collective responses to a tax reform are compared. We focus on the introduction of linear taxation in Germany. The exercise is replicated for other European countries and other topical reforms. Distortions due to the use of a unitary model turn out to be important in predicting labour supply adjustments, in the design of tax revenue neutral reforms, and in predicting a reform’s welfare implications.

British Local Government: A Case for a New Constitutional Settlement:

Abstract: As a creature of Statue, British local government is subject to constant change emanating from a superior constitutional source: central government. Much of the change that is imposed upon local government because of the need for governing institutions to respond to two competing sets of requirements: those that drive and are driven by either, technocracy or democracy. In all major reorganisations of local government, the attempts tofind a structuralfit between these two mutually antagonistic factors have seen the latter lose out to the former The question of local government size is part of the clash between technocracy and democracy that has been played-out in various reforms of local government in Britain. Indeed, current discussions about unitary councils and city-regions will ultimately result in larger, more remote and technocraticaly driven units of local governmentThe article sets out a construct for British local government that would rest on the creation of a new constitutional settlement betwee...

Does the representation of household behavior matter for welfare analysis of tax-benefit policies? An introduction

Abstract: A widely shared intuition holds that individual control over money matters for the decision process within the household and the subsequent distribution of resources and welfare. As a consequence, there are good reasons to depart from the unitary model of the household and to explore the possibilities offered by models of the family accounting for several decision makers in the household and for the potential impact of tax reforms on the balance of power. This paper summarizes both the methodological and empirical findings presented in the next three papers of this special issue of the Review of the Economics of the Household. This series of contributions primarily entails a concrete comparison of the policy implications of the choice between the unitary and a particular multi-person representation: the collective representation. On the one hand, it suggests a methodology to implement the collective model of labor supply in a realistic context where participation is modeled together with working hours, and where the full tax-benefit system is accounted for. On the other hand, the empirical part relies on comprehensive simulations of tax reforms in Belgium, France, Germany, Italy, Spain, and the United Kingdom, and allows to quantify the distortions that may affect policy recommendations based on the unitary model.

Unitary Space&#8211;Time Constellation Analysis: An Upper Bound for the Diversity

Abstract: The diversity product and the diversity sum are two very important parameters for a good-performing unitary space-time constellation. A basic question is what the maximal diversity product (or sum) is. In this correspondence, we are going to derive general upper bounds on the diversity sum and the diversity product for unitary constellations of any dimension n and any size m using packing techniques on the compact Lie group U(n)

Multipartite invariant states. I. Unitary symmetry

Abstract: We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of $d$-dimensional subsystems (qudits). These generalized states are invariant under the action of local unitary operations. We study basic properties of multipartite invariant states and present necessary and sufficient separability criteria.

Decompositions of unitary evolutions and entanglement dynamics of bipartite quantum systems

Abstract: We describe a decomposition of the Lie group of unitary evolutions for a bipartite quantum system of arbitrary dimensions. The decomposition is based on a recursive procedure that systematically uses the Cartan classification of the symmetric spaces of the Lie group SO(n). The resulting factorization of unitary evolutions clearly displays the local and entangling character of each factor.

p-Adic L-Functions for Unitary Shimura Varieties I: Construction of the Eisenstein Measure

Abstract: We construct the Eisenstein measure in several variables on a quasi-split unitary group, as a first step towards the construction of p-adic L-functions of families of ordinary holomorphic modular forms on unitary groups. The construction is a direct generalization of Katz' construction of p-adic L-functions for CM fields, and is based on the theory of p-adic modular forms on unitary Shimura varieties developed by Hida, and on the explicit calculation of non-degenerate Fourier coefficients of Eisenstein series.

Phase map decompositions for unitaries

Abstract: We propose a universal decomposition of unitary maps over a tensorial power of C^2, introducing the key concept of "phase maps", and investigate how this decomposition can be used to implement unitary maps directly in the measurement-based model for quantum computing. Specifically, we show how to extract from such a decomposition a matching entangled graph state (with inputs), and a set of measurements angles, when there is one. Next, we check whether the obtained graph state verifies a "flow" condition, which guarantees an execution order such that the dependent measurements and corrections of the pattern yield deterministic results. Using a graph theoretic characterization of flows, we can determine whether a flow can be constructed for a graph state in polynomial time. This approach yields an algorithmic procedure which, when it succeeds, may produce an efficient pattern for a given unitary.

Are Federal Systems Better than Unitary Systems

Abstract: Much has been written about the putative virtues and vices of federal and unitary systems of government, but little empirical testing of the impact of such systems on the quality of governance has been conducted. Do federal or unitary systems promote better social, political and economic outcomes? The paper takes up a series of theoretical debates put forth by advocates of federalism, including competition among subnational governments, fiscal federalism, veto points, accountability, and the size of government. In each case, there is room for doubt about the practical impact of federalism on governance. The paper then conducts a series of cross-national empirical tests over several decades of the impact of unitary systems on fifteen indicators of political, economic and human development. In most cases, a strong empirical relationship between unitarism and good governance obtains. To the extent that these constitutional structures make a difference, unitary systems appear to hold distinct advantages over federal ones.

Reduced 1-Cohomology of Connected Locally Compact Groups and Applications

Abstract: In this article we focus on the reduced 1-cohomology spaces of locally compact connected groups with coecients in unitary representations. The vanishing of these spaces for every unitary irreducible representation char- acterizes Kazhdan's property (T). The main theorem states that for a connected locally compact group, there are only a finite number of unitary irreducible rep- resentations for which the reduced 1-cohomology does not vanish. Moreover, a description of these representations is given.

A note on equivalence of bipartite states under local unitary transformations

Abstract: The equivalence of arbitrary dimensional bipartite states under local unitary transformations (LUT) is studied. A set of invariants and ancillary invariants under LUT is presented. We show that two states are equivalent under LUT if and only if they have the same values for all of these invariants.

Unitary spherical spectrum for split classical groups

Abstract: This paper gives a complete classification of the unitary irreducible spherical representations of split real and p-adic groups. The results were obtained around 2000, the changes to the new version are expository.

Spin networks and anyonic topological computing

Abstract: We review the q -deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups.

Summing norms of identities between unitary ideals

Abstract: Based on abstract interpolation, we prove asymptotic formulae for the (F,2)-summing norm of inclusions id: , where E and F are two Banach sequence spaces. Here, stands for the unitary ideal of operators on the n-dimensional Hilbert space whose singular values belong to E, and for the Hilbert-Schmidt operators. Our results are noncommutative analogues of results due to Bennett and Carl, as well as their recent generalizations to Banach sequence spaces. As an application, we give lower and upper estimates for certain s-numbers of the embeddings id: and id: . In the concluding section, we finally consider mixing norms.