Showing papers on "Unitary state published in 1995"
Book•
01 Jan 1995
TL;DR: The category C(g, K)IIIDuality Theorem IVReductive PairsVCohomological InductionVISignature TheoremVIITranslation FunctorsVIIIIrreducibility TheoremIXUnitarizability TheoremXMinimal K TypesXITransfer Theorem XIIEpilog: Weakly Unipotent RepresentationsApp. A. Distributions on ManifoldsApp. B. Elementary Homological AlgebraApp. C. Spectral Sequences
Abstract: PrefacePrerequisites by ChapterStandard NotationIntroductionIHecke AlgebrasIIThe Category C(g, K)IIIDuality TheoremIVReductive PairsVCohomological InductionVISignature TheoremVIITranslation FunctorsVIIIIrreducibility TheoremIXUnitarizability TheoremXMinimal K TypesXITransfer TheoremXIIEpilog: Weakly Unipotent RepresentationsApp. A. Miscellaneous AlgebraApp. B. Distributions on ManifoldsApp. C. Elementary Homological AlgebraApp. D. Spectral SequencesNotesReferencesIndex of NotationIndex
365 citations
TL;DR: In this article, the authors present a review of the family of matrix groups $Sp(2n,\Re)$ in a form suited to various applications both in optics and quantum mechanics.
Abstract: We present a utilitarian review of the family of matrix groups $Sp(2n,\Re)$, in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of $Sp(2n,\Re)$. Global decomposition theorems, interesting subgroups and their generators are described. Turning to $n$-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and develop a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under $Sp(2n,\Re)$ action are delineated.)
340 citations
TL;DR: The utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature is illustrated by generalizing linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions.
Abstract: Unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time, frequency, and scale. Implementation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing on the transformed signal, and then (in some cases) transforming the resulting output. The resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and, hence, prove useful for representing and processing signals that are not well matched by current techniques. As specific examples of this procedure, we generalize linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions. These applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature. >
235 citations
Posted Content•
TL;DR: The overall conclusion is that almost all problems are hard to solve with quantum circuits, including decision problem and guess checkable functions.
Abstract: In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower bounds on the approximation capabilities of g-qubit unitary operations for fixed g. We consider approximation of unitary operations on subspaces as well as approximation of states and of density matrices by quantum circuits in several natural metrics. The ability of quantum circuits to probabilistically solve decision problem and guess checkable functions is discussed. We also address exact unitary representation by reducing the upper bound by a factor of n^2 and by formalizing the argument given by Barenco et al. [1995] for the lower bound. The overall conclusion is that almost all problems are hard to solve with quantum circuits.
161 citations
31 Jan 1995
157 citations
TL;DR: In this article, the authors argue that the polysemy view is not capable of giving a unified account of the meanings of CAN, MAY, MUST and SHOULD, whereas the unitary meaning view does not encounter the problems facing the polysemmy view and propose unitary meanings which are rich enough to account for the range of interpretations these modals can have, but which are specific enough to explain why they get these interpretations and not others.
Abstract: In this paper I argue that the polysemy view is not capable of giving a unified account of the meanings of CAN, MAY, MUST and SHOULD, whereas the unitary meaning view does not encounter the problems facing the polysemy view. I propose unitary meanings which are rich enough to account for the range of interpretations these modals can have, but which are specific enough to account for why they get these interpretations and not others. Proposing unitary meanings implies that we have to look for a theory of pragmatics which can explain how we achieve the different interpretations of these modals in use. I will argue that adopting the Relevance theory view of what drives interpretation gives us the basis for such an explanation.
100 citations
TL;DR: The history of modem China, in the round, is recounted as a struggle for national reunification and liberation traced through the rise and fall of successive state formations in the imperial, early Republican (1912-27), Nationalist (1928-49) and Communist periods as mentioned in this paper.
Abstract: The history of modem China, in the round, is recounted as a struggle for national reunification and liberation traced through the rise and fall of successive state formations in the imperial, early Republican (1912-27), Nationalist (1928-49) and Communist periods. What lends continuity to this history from one regime to the next is the motif of a unitary state reconstituting itself from the rubble of a disintegrating empire. Continuity derives as well from an implicit identification of the unitary state with the nation on whose behalf the state is presumed to act: the ideal of the unitary state is linked with the idea of a national people firstly in the story of their common struggle and secondly in the assumption that the one, the state, 'represents' the other, the nation. The nation is presumed to be as continuous as the hoary ideal of the unitary state itself despite the relatively recent vintage of the concept of the nation in China, despite the equally recent genesis of the idea that the state should represent anything at all, and despite the
91 citations
44 citations
25 May 1995
39 citations
Book•
01 Apr 1995
TL;DR: In 1981, the newly elected socialist government of France announced a "vast programme of decentralization" as mentioned in this paper, which has changed the politico-administrative landscape of France.
Abstract: In 1981, the newly elected socialist government of France announced a "vast programme of decentralization". The reforms have changed the politico-administrative landscape of France. This volume asks what changes - if any - occurred and looks at the implications for French public policy-making.
Journal Article•
TL;DR: In this article, the authors analyze nonabelian massive Higgs-free theories in the causal Epstein-Glaser approach and explicitly show the reason why the considered models fail to be unitary.
Abstract: We analyze nonabelian massive Higgs-free theories in the causal Epstein-Glaser approach. Recently, there has been renewed interest in these models. In particular we consider the well-known Curci-Ferrari model and the nonabelian St\"uckelberg models. We explicitly show the reason why the considered models fail to be unitary. In our approach only the asymptotic (linear) BRS-symmetry has to be considered.
TL;DR: In this paper, it was shown that for large n and large irreducible representations of a unitary group U(n) the measure associated to the tensor product of two representations, or to the restriction of a representation to a subgroup U(m) with m comparable to n, can be expressed in terms of the measures associated to first representations by means of the notion of free convolution.
Abstract: To each finite dimensional representation of a unitary group U(n) is associated a probability measure on the set of integers, depending on the highest weights which occur in this representation. We show that asymptotically for large n and large irreducible representations of U(n) the measure associated to the tensor product of two representations, or to the restriction of a representation to a subgroup U(m) with m comparable to n, can be expressed in terms of the measures associated to the first representations by means of the notion of free convolution (namely additive free convolution for the tensor product problem and multiplicative free convolution for the restriction problem).
01 Apr 1995
TL;DR: In this paper, the reducibility and number of components of any representation of a quasi-split unitary group which is parabolically induced from a discrete series representation is determined.
Abstract: We determine the reducibility and number of components of any representation of a quasi-split unitary group which is parabolically induced from a discrete series representation. The R-groups are computed explicitly, in terms of reducibility for maximal parabolics. This gives a description of the elliptic representations.
TL;DR: A QR-like algorithm, called the con-QR algorithm, for computing the Youla form of a general complex matrix is presented, an analog of the Schur form where unitary congruences instead of unitary similarities are employed.
Abstract: In this paper, a QR-like algorithm, called the con-QR algorithm, for computing the Youla form of a general complex matrix is presented. The Youla form is an analog of the Schur form where unitary congruences instead of unitary similarities are employed. We introduce a set of invariants of a unitary congruence transformation which are called coneigenvalues, and discuss their condition. Finally, the practical value of the Youla form is discussed.
TL;DR: SecondR-quantization as mentioned in this paper is a deformation of the standard second quantization which properly takes into account the nontrivial exchange properties characterizing generalized statistics and the Euclidean covariance of anyons.
Abstract: We investigate the notion of secondR-quantization - a suitable deformation of the standard second quantization which properly takes into account the nontrivial exchange properties characterizing generalized statistics. We also perform theR-quantization of a class of unitary one-particle representations relevant for the description of symmetries. The Euclidean covariance of anyons is analyzed within this context.
TL;DR: In this article, the current circumstances surrounding the changing role of the state in ocean affairs are briefly considered, including technological and economic factors, with particular reference to the types of state involved, be these unitary, federal, centrally planned or developing.
TL;DR: Unitary irreducible representations of a independent q-oscillators were used for the construction of all unitary irreducerible representations as discussed by the authors for the SUq(n)-covariant system of q-scillators.
Abstract: Unitary irreducible representations of a independent q-oscillators are used for the construction of all unitary irreducible representations of the SUq(n)-covariant system of q-oscillators.
TL;DR: In this article, the problem of determining whether a unitary element is a product of Cayley unitary elements is completely solved for simple artinian rings of characteristic not 2. Theorem 1.
TL;DR: The paper shows how the minimal estimation error depends on a bound on data perturbations and specify the form of an optimal algorithm, with applications to recovering band-limited signals.
Abstract: The paper deals with estimating linear continuous functionals on unitary spaces from inaccurate information, with applications to recovering band-limited signals. We show how the minimal estimation error depends on a bound on data perturbations and specify the form of an optimal algorithm.
TL;DR: In this article, a general review of matrix groups in general matrices is presented, in a form suited to various applications both in optics and quantum mechanics, where the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of the matrix groups.
Abstract: text of abstract (We present a utilitarian review of the family of matrix groups $Sp(2n,\Re)$, in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of $Sp(2n,\Re)$. Global decomposition theorems, interesting subgroups and their generators are described. Turning to $n$-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and develop a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under $Sp(2n,\Re)$ action are delineated.)
Posted Content•
TL;DR: In this article, it was shown that any unitary or anti-unitary operator under whose adjoint action any algebra of local observables is mapped onto an algebra which can be localized in Minkowski space can be fixed up to some translation.
Abstract: Recently Borchers has shown that in a theory of local observables, certain unitary and antiunitary operators, which are obtained from an elementary construction suggested by Bisognano and Wichmann, commute with the translation operators like Lorentz boosts and \pct-operators, respectively. We conclude from this that as soon as the operators considered implement {\em any} symmetry, this symmetry can be fixed up to at most some translation. As a symmetry, we admit any unitary or antiunitary operator under whose adjoint action any algebra of local observables is mapped onto an algebra which can be localized somewhere in Minkowski space.
TL;DR: The authors argue that the only basis for a common ethnicity is their continuing engagement in the challenge of maintaining a political community in which they can accomplish significant civic tasks together while respecting their multiple identities.
Abstract: Attempts to establish a unitary sense of Canadian citizenship through symbolic engineering at the constitutional level are self‐defeating. Canadians must accept that their only basis for a common ethnicity is their continuing engagement in the challenge of maintaining a political community in which they can accomplish significant civic tasks together while respecting their multiple identities.
01 Jan 1995
TL;DR: In this paper, all near-rings are left distributive zero-symmetric and have an identity, and all N-groups are unitary, making use of conventions, notation and definitions from [17].
Abstract: Throughout this paper all near-rings are left distributive zero-symmetric and have an identity. Also all N-groups will be unitary. In this and other regards we shall be making use of conventions, notation and definitions from [17].
TL;DR: In this article, it was shown that the "guonic" formalism based on a g -operator deformation of the Heisenberg-Weyl algebra preserves, under a Jordan-Schwinger map, unitary (U(N)) and pseudounitary (SU(1, 1)) symmetries.
14 Feb 1995
TL;DR: In this article, the authors examined the physical application of deformations of Lie algebras and their use in generalising some exotic quantum optical states, and proposed a new unitary operator which is a q-analogue of the displacement operator of conventional coherent state theory: this is used to construct q-displaced vacuum states which are eigenstates of the annihilation operator.
Abstract: This subject of this thesis is the physical application of deformations of Lie algebras and their use in generalising some exotic quantum optical states.
We begin by examining the theory of quantum groups and the q-boson algebras used in their representation theory. Following a review of the properties of conventional coherent states, we describe the extension of the theory to various deformed Heisenberg-Weyl algebras, as well as the q-deformations of su(2) and su(1,1). Using the Deformed Oscillator Algebra of Bonatsos and Daskaloyannis, we construct generalised deformed coherent states and investigate some of their quantum optical properties. We then demonstrate a resolution of unity for such states and suggest a way of investigating the geometric effects of the deformation.
The formalism devised by Rembielinski et al is used to consider coherent states of the q-boson algebra over the quantum complex plane. We propose a new unitary operator which is a q-analogue of the displacement operator of conventional coherent state theory: This is used to construct q-displaced vacuum states which are eigenstates of the annihilation operator. Some quantum mechanical properties of these states are investigated and it is shown that they formally satisfy a Heisenberg-type minimum uncertainty relation.
After briefly reviewing the theory of conventional squeezed states, we examine the various q-generalisations. We propose a q-analogue of the squeezed vacuum state, and use this in conjunction with the unitary q-displacement operator to construct a general q-squeezed state, parameterised by noncommuting variables.. It is shown that, like their conventional counterparts, such states satisfy the Robertson-Schrodinger Uncertainty Relation.
We conclude with a brief discussion about the appearance of noncommuting variables in the states that have been considered.