Showing papers on "Unitary state published in 2004"
TL;DR: In this paper, the geometry of the coherence vector for n-level quantum systems is studied and a detailed analysis of the three-level case is presented, and a refined stratification in terms of symplectic orbits is considered.
Abstract: Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than 2. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence vector for n-level quantum systems. It is shown that the unitary orbits can be naturally identified with spheres in only for n = 2. In higher dimensions the coherence vector only defines a non-surjective embedding into a closed ball. A detailed analysis of the three-level case is presented. Finally, a refined stratification in terms of symplectic orbits is considered.
75 citations
TL;DR: For the quasi-split unitary group U(n,n), a refined analogue of the result of Kudla and Rallis on an identity (a regularized Siegel-Weil formula) between a residue of an Eisenstein series and the integral of a certain theta function was shown in this paper.
Abstract: For the quasi-split unitary group U(n,n), we prove a refined analogue of the result of S. S. Kudla and S. Rallis on an identity (a regularized Siegel-Weil formula) between a residue of an Eisenstein series and the integral of a certain theta function.
70 citations
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TL;DR: In this article, the authors derived a unitary solution of the Quantum Yang-Baxter equation via Yang--Baxterization and constructed the Hamiltonian responsible for the time-evolution of the unitary braiding operator.
Abstract: It is fundamental to view unitary braiding operators describing topological entanglements as universal quantum gates for quantum computation. This paper derives a unitary solution of the Quantum Yang--Baxter equation via Yang--Baxterization and constructs the Hamiltonian responsible for the time-evolution of the unitary braiding operator.
66 citations
TL;DR: In this article, the problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed, and it is shown that by using nonseparable measurements one can improve the accuracy of the estimation by a factor of 2(d+1)/d where d is the dimension of the Hilbert space on which U acts.
Abstract: The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts, and then measure the joint output state. This measurement could be an entangled one or it could be separable (e.g., measurements which can be implemented with local operations and classical communication or LOCC). A comparison is made between these possibilities and it is shown that by using nonseparable measurements one can improve the accuracy of the estimation by a factor of 2(d+1)/d where d is the dimension of the Hilbert space on which U acts.
61 citations
TL;DR: The authors examines the paradox of how federal political institutions are created: how can a state-building core be unyielding enough to forge a union but accommodating enough to grant federal concessions to subunits?
Abstract: This article examines the paradox of how federal political institutions are created: how can a state-building core be unyielding enough to forge a union but accommodating enough to grant federal concessions to subunits? A comparison of the trajectories of national unification in nineteenth-century Germany and Italy indicates that the formation of federations does not come about exclusively through voluntary “contract”; instead, coercion and cooperation go hand in hand in the formation of all states, including federations. Whether the outcome is federal or unitary depends on the level of subunit infrastructural capacity at the moment of founding.The article finds that where the constituents of a potential federation are parliamentary and well governed, they can deliver the benefits of state formation, assuring their continued existence in a federation. Where such subunits are patrimonial and poorly governed, they are absorbed within a unitary model of governance. This institutional explanation supplements accounts emphasizing the cultural sources of federalism and revises arguments that only militarily weak founding cores make federal concessions to their constituents.
58 citations
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TL;DR: In this article, the authors give a proof of universality for orthogonal and symplectic ensembles of random matrices in the scaling limit for a class of weights w(x)=exp(-V(x)) where V is a polynomial, V(x) =kappa(2m)x^{2m}+..., kappa( 2m)>0.
Abstract: We give a proof of the Universality Conjecture for orthogonal and symplectic ensembles of random matrices in the scaling limit for a class of weights w(x)=exp(-V(x)) where V is a polynomial, V(x)=kappa_{2m}x^{2m}+..., kappa_{2m}>0. For such weights the associated equilibrium measure is supported on a single interval. The precise statement of our results is given in Theorem 1.1 below. For a proof of the Universality Conjecture for unitary ensembles, for the same class of weights, see [DKMVZ2].
Our starting point is Widom's representation [W] of the orthogonal and symplectic correlation kernels in terms of the kernel arising in the unitary case plus a correction term which is constructed out of derivatives and integrals of orthonormal polynomials (OP's) {p_j(x)}, j=0,1,..., with respect to the weight w(x). The calculations in [W] in turn depend on the earlier work of Tracy and Widom [TW2]. It turns out (see [W] and also Theorems 2.1 and 2.2 below) that only the OP's in the range j=N+O(1), N->infinity, contribute to the correction term. In controlling this correction term, and hence proving Universality for both the orthogonal and symplectic cases, the uniform Plancherel--Rotach type asymptotics for the OP's found in [DKMVZ2] play an important role, but there are significant new analytical difficulties that must be overcome which are not present in the unitary case. We note that we do not use skew orthogonal polynomials.
54 citations
TL;DR: The role of performance and theater as a means of generating cooperation within a diverse transnational movement, on intramovement conflict, and on the role of the state with respect to transnational protest is discussed in this paper.
Abstract: Transnational antiglobalization protests have become a hallmark of global activism since 1999 Over this time, the transnational protest movement has generated its own internal and external dynamics of conflict and cooperation, playing them out on a global scale This essay addresses these dynamics, focusing on the role of performance and theater as a means of generating cooperation within a diverse transnational movement, on intramovement conflict, and on the role of the state with respect to transnational protest By breaking down dominant conceptions of the state as a unitary actor, transnational protests have helped fuel an as yet understudied form of cooperation: that among policing agencies, across local and national levels of law enforcement, and across national borders Cross-national police cooperation has become particularly important in the context of the war against terrorism However, it has also been shaped by the need to maintain public order that has arisen as a result of the large, and often disruptive, street protests against globalization, which have involved activists from many countries
53 citations
TL;DR: In this article, the positive and not completely positive maps of density matrices are discussed and the probability representation of spin states (spin tomography) is reviewed and a U(N)-tomogram of photon state in Fock basis is constructed.
53 citations
Abstract: The two-qubit canonical decomposition SU(4)=[SU(2)⊗SU(2)]Δ[SU(2)⊗SU(2)] writes any two-qubit unitary operator as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary. Using Lie theory, we generalize this to an n-qubit decomposition, the concurrence canonical decomposition (CCD) SU(2n)=KAK. The group K fixes a bilinear form related to the concurrence, and in particular any unitary in K preserves the tangle |〈φ|¯(−iσ1y)⋯(−iσny)|φ〉|2 for n even. Thus, the CCD shows that any n-qubit unitary is a composition of a unitary operator preserving this n-tangle, a unitary operator in A which applies relative phases to a set of GHZ states, and a second unitary operator which preserves the tangle. As an application, we study the extent to which a large, random unitary may change concurrence. The result states that for a randomly chosen a∈A⊂SU(22p), the probability that a carries a state of tangle 0 to a state of maximum tangle approaches 1 as the even number of qubits approach...
52 citations
TL;DR: In every modern political system, power is shared to a greater or lesser extent between levels of government as discussed by the authors, and power sharing arrangements are perhaps most explicit in formal federal systems like the United States and Canada, where federal constitutions define the relative powers of central and subnational governments.
Abstract: In every modern political system, power is shared to a greater or lesser extent between levels of government. These power sharing arrangements are perhaps most explicit in formal federal systems like the United States and Canada, where federal constitutions define the relative powers of central and subnational governments. They may be no less important, however, in unitary democracies and even authoritarian regimes where central governments require local actors to implement policy on the ground and often delegate significant authority to them. Indeed, in any large and complex modern society, effective governance requires some sharing of power between higher levels of government, capable of coordinating many disparate actors and interests, and lower levels of government, capable of responding to local conditions.
52 citations
TL;DR: Novel means are being developed on single Internet sites to retain the diversity of multiple concepts for taxa, providing hope that taxonomy may become established as a Web-based information discipline that will unify the discipline and facilitate data access.
Abstract: Taxonomic data form a substantial, but scattered, resource. The alternative to such a fragmented system is a 'unitary' one of preferred, consensual classifications. For effective access and distribution the (Web) revision for a given taxon would be established at a single Internet site. Although all the international codes of nomenclature currently preclude the Internet as a valid medium of publication, elements of unitary taxonomy (UT) still exist in the paper system. Much taxonomy, unitary or not, already resides on the Web. Arguments for and against adopting a unitary approach are considered and a resolution is attempted. Rendering taxonomy essentially Web-based is as inevitable as it is desirable. Apparently antithetical to the UT proposal is the view that in reality multiple classifications of the same taxon exist, since different taxonomists often hold different concepts of their taxa: a single name may apply to many different (frequently overlapping) circumscriptions and more than one name to a single taxon. However, novel means are being developed on single Internet sites to retain the diversity of multiple concepts for taxa, providing hope that taxonomy may become established as a Web-based information discipline that will unify the discipline and facilitate data access.
TL;DR: Using the notion of symplectic structure and Weyl product of non-commutative geometry, the authors construct unitary representations for the Galilei group and show how to rewrite the Schrodinger equation in phase space.
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TL;DR: In this paper, it was shown that the simplest band representations of unitary operators on a Hilbert space are five-diagonal, and a parametrization of such representations was provided.
Abstract: In this paper we prove that the simplest band representations of unitary operators on a Hilbert space are five-diagonal. Orthogonal polynomials on the unit circle play an essential role in the development of this result, and also provide a parametrization of such five-diagonal representations which shows specially simple and interesting decomposition and factorization properties. As an application we get the reduction of the spectral problem of any unitary Hessenberg matrix to the spectral problem of a five-diagonal one. Two applications of these results to the study of orthogonal polynomials on the unit circle are presented: the first one concerns Krein's Theorem; the second one deals with the movement of mass points of the orthogonality measure under monoparametric perturbations of the Schur parameters.
TL;DR: In this paper, the quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations, which can be used as a pedagogical introduction to the unitary transformation.
Abstract: The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various approximation schemes. Due to its simplicity, it can be used as a pedagogical introduction to the unitary transformations. Both the spectrum and the spectral weights are discussed.
TL;DR: In this article, the density of states measure for a class of random unitary band matrices is studied and a Thouless formula relating it to the associated Lyapunov exponent is derived.
Abstract: We study the density of states measure for some class of random unitary band matrices and prove a Thouless formula relating it to the associated Lyapunov exponent. This class of random matrices appears in the study of the dynamical stability of certain quantum systems and can be considered as a unitary version of the Anderson model. It is also related with orthogonal polynomials on the unit circle. We further determine the support of the density of states measure and provide a condition ensuring it possesses an analytic density.
TL;DR: In this paper, the necessary and sufficient condition for the reproducibility of the original classical games is presented, which implies that complete orthogonal bases can be constructed from a given multipartite entangled state provided that each party is restricted to two local unitary operators, and it is shown that most states belonging to the class of symmetric states with respect to permutations, including the N-qubit W state, do not satisfy this condition.
TL;DR: This work describes the use and design of trellis-coded space- time modulation schemes that use unitary space-time constellations and studies the performance of treller-coded unitaryspace-time modulation for block fading channels under the assumption of no channel state information.
Abstract: Space-time coding is well established for high data rate communications over wireless channels with perfect channel state information. On the other hand, the case where the channel state information is unknown has received limited attention. Recently, a new signaling scheme called unitary space-time modulation that is suitable for the latter case has been proposed. We describe the use and design of trellis-coded space-time modulation schemes that use unitary space-time constellations. We construct these codes using a novel suboptimal code design criteria and study the performance of trellis-coded unitary space-time modulation for block fading channels under the assumption of no channel state information. Simulation results show that the proposed schemes improve the performance compared to uncoded transmission with the same spectral efficiency. The results are also compared with the turbo-coded modulation scheme Bahceci (2002) and the differential detection scheme described Jafarkhani (2001) under the same assumptions.
01 Jan 2004
TL;DR: The authors showed that in many languages, such as Russian and Chinese, there is more semantic structure than meets the eye than appears on the surface; they are simply unpronounced lexical items.
Abstract: Philosophers of language (and semanticists) do not agree on much, but few have felt reason to doubt that there are at least two kinds of descriptions in natural language: deWnite descriptions (e.g. of the form ‘the F ’), used in sentences which say that there is a unique satisWer of F, and indeWnite descriptions (e.g. of the form ‘an F ’), used in sentences which claim only that something or other satisWes F. However, if analytic philosophy had spawned in languages other than English and German, this assumption might not appear so innocent. In many languages—even many Indo-European languages—we do not Wnd these two kinds of descriptions, at least not on the surface. In Russian, for example, neither deWnite nor indeWnite articles appear on the surface: ‘the man’ and ‘a man’ would both be expressed by the Russian equivalent of ‘man’. If we suppose that natural languages do not diVer from each other in their logical form,1 then there are a limited number of possible paths we can take to explain the discrepancy between English and these other languages. The Wrst path is simply to say that, for example, Russian has both deWnite and indeWnite descriptions, but that they do not appear on the surface; they are simply unpronounced lexical items. In other words, in Russian and similar languages, there is more semantic structure than meets the eye.
TL;DR: In this paper, the authors consider an economy that incorporates cross-border shopping and where the different levels of government are concerned with the well-being of their citizens, and show how the central government as a Stackelberg leader can adjust its fiscal instruments so that the tax externalities are also internalised.
01 Jan 2004
TL;DR: The vertical structure of government in all OECD countries is characterized by a hierarchy of two or three layers of governments, with the national government at the top and local governments at the bottom as mentioned in this paper.
Abstract: The vertical structure of government in all OECD countries is characterized by a hierarchy of two or three layers of governments, with the national government at the top and local government at the bottom. Typically, unitary states like Sweden have two layers, while federal states like Germany have three layers of more. This structure serves as a basis for assigning specific tasks to local governments, which, due to their closer proximity to the citizen and their better knowledge of local economic conditions, they can fulfil better than the central government.1 Decentralization of the public sector also serves to create competition for taxpayers among local governments. Such competition is regarded as a check on rent-seeking behavior of selfish politicians and on excessive growth of government.2
TL;DR: In this paper, the authors characterize the resource allocations in both a unitary and a federal state, and identify the set of instruments that are required to replicate the social optimum in each state.
Abstract: A two-region economy consists of a given but different number of immobile workers in each region, and a given number of mobile firms. Firms create jobs where they locate, but there is frictional unemployment. Two sorts of agglomeration effects arise: those from economies of scale in matching, and those from production economies external to the firm. Regions may either be part of a unitary state in which case all regional policies are decided by the central government, or they may be part of a federal state in which case some policies are determined by the regional governments. We characterize the resource allocations in both a unitary and a federal state, and identify the set of instruments that are required to replicate the social optimum in each state.
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TL;DR: The universal symmetry of complexity of complexity as mentioned in this paper provides a universal definition of randomness, probability, chaoticity, complexity, fractality, self-organisation, and other properties.
Abstract: The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived, universal definitions of randomness, probability, chaoticity, complexity, fractality, self-organisation, and other properties, extending their axiomatic introduction in the conventional, dynamically single-valued (unitary) theory (physics/9806002, physics/0211071). Any real system emergence, structure, and behaviour can be expressed now by the universal law of conservation, or symmetry, of complexity that unifies extended versions of any (correct) symmetry, law, or "principle". Both the observed world structure and its unreduced dynamics result from that universal, unique symmetry, instead of formal imposition of separated, broken and simplified symmetries upon the existing, postulated structures in the unitary world "model". Whereas any unitary "symmetry" is regular and therefore practically always "spontaneously broken" (violated) in the real world dynamics, the universal symmetry of complexity remains always exact, but unites different, irregular, dynamically nonlinear, and intrinsically unstable patterns of unreduced world structure. It also provides the rigorous, dynamically derived expression of the ``arrow of time" (generalised entropy growth law) applicable to any real, necessarily complex system, from elementary particle to the universe. Particular applications of the universal symmetry of complexity, from fundamental physics to biology and theory of consciousness, provide old mysteries solutions and new research perspectives.
TL;DR: In this paper, the summands in the Wold decomposition of a bi-isometry were characterized using the unitary model associated to a biisometry, which appears for the first time in [1] and was recently rediscovered in [2].
Abstract: In this work we use the unitary model associated to a bi-isometry, which appears for the first time in [1] and was recently rediscovered in [2], to characterize the summands in the Wold decompositions of a bi-isometry and to give new proofs of such decomposition theorems.
Journal Article•
TL;DR: Using a geometric approach, the minimum number of applications needed for an arbitrary controlled-unitary gate to construct a universal quantum circuit is derived and shown to be either optimal or close to optimal.
Abstract: Using a geometric approach, we derive the minimum number of applications needed for an arbitrary controlled-unitary gate to construct a universal quantum circuit. An analytic construction procedure is presented and shown to be either optimal or close to optimal. This result can be extended to improve the efficiency of universal quantum circuit construction from any entangling gate. In addition, for both the controlled-NOT (CNOT) and double-cNoT gates, we develop simple analytic ways to construct universal quantum circuits with three applications, which is the least possible for these gates.
01 Dec 2004
TL;DR: Unitary Development Plan - Merton's development plan set out in full and by chapter (PDF format) as mentioned in this paper, which is a summary of the development plan of the United States.
Abstract: Unitary Development Plan - Merton's development plan set out in full and by chapter (PDF format)
TL;DR: In this article, the positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R) were classified.
Abstract: We give the classification of the positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R).
TL;DR: This paper shows the relevance of the multisemilattice structure in the design of algorithms aimed at calculating unitary implicates and implicants in temporal logics and offers an equivalent algebraic characterization based on non-deterministic operators and with a weakly associative property.
Abstract: The concepts of implicates and implicants are widely used in several fields of “Automated Reasoning”. Particularly, our research group has developed several techniques that allow us to reduce efficiently the size of the input, and therefore the complexity of the problem. These techniques are based on obtaining and using implicit information that is collected in terms of unitary implicates and implicants. Thus, we require efficient algorithms to calculate them. In classical propositional logic it is easy to obtain efficient algorithms to calculate the set of unitary implicants and implicates of a formula. In temporal logics, contrary to what we see in classical propositional logic, these sets may contain infinitely many members. Thus, in order to calculate them in an efficient way, we have to base the calculation on the theoretical study of how these sets behave. Such a study reveals the need to make a generalization of Lattice Theory, which is very important in “Computational Algebra”. In this paper we introduce the multisemilattice structure as a generalization of the semilattice structure. Such a structure is proposed as a particular type of poset. Subsequently, we offer an equivalent algebraic characterization based on non-deterministic operators and with a weakly associative property. We also show that from the structure of multisemilattice we can obtain an algebraic characterization of the multilattice structure. This paper concludes by showing the relevance of the multisemilattice structure in the design of algorithms aimed at calculating unitary implicates and implicants in temporal logics. Concretely, we show that it is possible to design efficient algorithms to calculate the unitary implicants/implicates only if the unitary formulae set has the multisemilattice structure.
TL;DR: In this paper, a model where the power to set policy (a choice of project) may be assigned to central or regional government via either a federal or unitary referendum is studied, where the benefit of central provision is an economy of scale, while the cost is political inefficiency.
Abstract: This paper studies a model where the power to set policy (a choice of project) may be assigned to central or regional government via either a federal or unitary referendum. The benefit of central provision is an economy of scale, while the cost is political inefficiency. The relationship between federal and unitary referenda is characterized in the asymptotic case as the number of regions becomes large, under the assumption that the median project benefit in any region is a random draw from a fixed distribution, G. Under some symmetry assumptions, the relationship depends only on the shape of G, not on how willingness to pay is distributed within regions. The relationship to Cremer and Palfrey’s “principle of aggregation” is established. Asymptotic results on the efficiency of the two referenda are also proved.
TL;DR: In this paper, a unitary approach to the construction of representations and intertwining operators is presented, and applied to the C*-algebras, groups, Gabor-type unitary systems and wavelets.
Abstract: We present a unitary approach to the construction of representations and intertwining operators. We apply it to the C*-algebras, groups, Gabor-type unitary systems and wavelets. We give an application of our method to the theory of frames, and we prove a general dilation theorem which is in turn applied to specific cases, and we obtain in this way a dilation theorem for wavelets.
TL;DR: For the Stokes tensor parametrization of a multiqubit density operator, the authors provides an explicit formulation of the corresponding unitary dynamics at the infinitesimal level.
Abstract: For the Stokes tensor parametrization of a multiqubit density operator, we provide an explicit formulation of the corresponding unitary dynamics at the infinitesimal level. The main advantage of this formalism (clearly reminiscent of the ideas of ``coherences'' and ``coupling Hamiltonians'' of spin systems) is that the pattern of correlation between qubits and the pattern of infinitesimal correlation are highlighted simultaneously and can be used constructively for qubit manipulation. For example, it allows us to compute explicitly Rodrigues' formula for the one-parameter orbits of nonlocal Hamiltonians. The result is easily generalizable to orbits of Cartan subalgebras and allows us to express the Cartan decomposition of unitary propagators as a linear action directly in terms of the infinitesimal generators.