Topic
Unitary state
About: Unitary state is a research topic. Over the lifetime, 4651 publications have been published within this topic receiving 72606 citations.
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TL;DR: In this article, it was shown that all minimum-uncertainty packets are unitarily equivalent to the coherent states and that coherence may be viewed as stationary minimality, and a new calculation of some matrix elements of the operator that implements the unitary equivalence was given.
Abstract: In a previous paper we have shown that all minimum-uncertainty packets are unitarily equivalent to the coherent states and that coherence may be viewed as stationary minimality. In this note we give some additional information relating to the nature of the unitary-equivalence structure. We also give a new calculation of some matrix elements of the operator that implements the unitary equivalence which is not subject to the shortcoming inherent in the original calculation.
565 citations
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01 Jan 2000TL;DR: In this article, a basic theory for frames and complementary frames and disjointness of unitary systems is presented. But this theory is not applicable to unitary system models.
Abstract: Introduction Basic theory for frames Complementary frames and disjointness Frame vectors for unitary systems Gabor type unitary systems Frame wavelets, super-wavelets and frame sets Frame representations for groups Concluding remarks Bibliography.
559 citations
01 May 1985
TL;DR: A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states.
Abstract: A new formalism for analyzing two-photon devices, such as parametric amplifiers and phase-conjugate mirrors, is proposed in part I, focusing on the properties and the significance of the quadrature-phase amplitudes and two-mode squeezed states. Time-stationary quasi-probability noise is also detailed for the case of Gaussian noise, and uncertainty principles for the quadrature-phase amplitudes are outlined, as well as some important properties of the two-mode states. Part II establishes a mathematical foundation for the formalism, with introduction of a vector notation for compact representation of two-mode properties. Fundamental unitary operators and special quantum states are also examined with an emphasis on the two-mode squeezed states. The results are applied to a previously studied degenerate limit (epsilon = 0).
539 citations
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TL;DR: Though this result raises questions about NMR quantum computation, further analysis would be necessary to assess the power of the general unitary transformations, which are indeed implemented in these experiments, in their action on separable states.
Abstract: We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable (unentangled). The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. The bounds show that no entanglement appears in the physical states at any stage of present NMR experiments. Though this result raises questions about NMR quantum computation, further analysis would be necessary to assess the power of the general unitary transformations, which are indeed implemented in these experiments, in their action on separable states.
525 citations
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TL;DR: The authors argue that the notion of multiple semantics does not represent a theory of semantic organisation but is, instead, an arbitrary conjunction of a set of independent assumptions which are either unmotivated or, if motivated, equally compatible with a unitary semantics hypothesis.
Abstract: In this paper we discuss the issue of multiple versus unitary semantics. We argue that the notion of multiple semantics (as currently articulated) does not, in fact, represent a theory of semantic organisation but is, instead, an arbitrary conjunction of a set of independent assumptions which are either unmotivated or, if motivated, equally compatible with a unitary semantics hypothesis. Furthermore, the empirical evidence that has been cited as support for this hypothesis is equally compatible with variants of the unitary semantics hypothesis. A model of semantic processing—the Organised Unitary Content Hypothesis (O.U.C.H.)—that is able to account for reported patterns of dissociation of performance is discussed briefly.
525 citations