Are Coherent States the Natural Language of Quantum Theory?

From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT

Journal of High Energy Physics ◽

10.1007/jhep12(2020)185 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Alexandre Belin ◽

Benjamin Withers

Keyword(s):

Quantum Theory ◽

Initial Data ◽

Path Integral ◽

Coherent States ◽

Microscopic Theory ◽

Delta Function ◽

Common Method ◽

Single Trace

Abstract A common method to prepare states in AdS/CFT is to perform the Euclidean path integral with sources turned on for single-trace operators. These states can be interpreted as coherent states of the bulk quantum theory associated to Lorentzian initial data on a Cauchy slice. In this paper, we discuss the extent to which arbitrary initial data can be obtained in this way. We show that the initial data must be analytic and define the subset of it that can be prepared by imposing bulk regularity. Turning this around, we show that for generic analytic initial data the corresponding Euclidean section contains singularities coming from delta function sources in the bulk. We propose an interpretation of these singularities as non-perturbative objects in the microscopic theory.

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SUSY coherent states and enhanced canonical quantizations for Pauli model

International Journal of Modern Physics A ◽

10.1142/s0217751x21501050 ◽

2021 ◽

pp. 2150105

Author(s):

Jean Vignon Hounguevou ◽

Daniel Sabi Takou ◽

Gabriel Y. H. Avossevou

Keyword(s):

Quantum Mechanics ◽

Quantum Theory ◽

Coherent States ◽

Differential Operators ◽

Canonical Quantization ◽

Point Of View ◽

Supersymmetric Quantum Mechanics ◽

Geometric Properties

In this paper, we study coherent states for a quantum Pauli model through supersymmetric quantum mechanics (SUSYQM) method. From the point of view of canonical quantization, the construction of these coherent states is based on the very important differential operators in SUSYQM call factorization operators. The connection between classical and quantum theory is given by using the geometric properties of these states.

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Quantum theory of unambiguous measurements

Acta Physica Slovaca Reviews and Tutorials ◽

10.2478/v10155-010-0099-3 ◽

2009 ◽

Vol 59 (6) ◽

Cited By ~ 11

Author(s):

Michal Sedlák

Keyword(s):

Quantum Theory ◽

Finite Number ◽

Coherent States ◽

Single Mode ◽

Linear Optics ◽

Optical Fields ◽

Optimal Test ◽

Unknown State ◽

Multiple Copies ◽

The Difference

Quantum theory of unambiguous measurementsIn the present paper I formulate a framework that accommodates many unambiguous discrimination problems. I show that the prior information about any type of constituent (state, channel, or observable) allows us to reformulate the discrimination among finite number of alternatives as the discrimination among finite number of average constituents. Using this framework I solve several unambiguous tasks. I present a solution to optimal unambiguous comparison of two ensembles of unknown quantum states. I consider two cases: 1) The two unknown states are arbitrary pure states of qudits. 2) Alternatively, they are coherent states of single-mode optical fields. For this case I propose simple and optimal experimental setup composed of beam-splitters and a photodetector. As a second tasks I consider an unambiguous identification (UI) of coherent states. In this task identical quantum systems are prepared in coherent states and labeled as unknown and reference states, respectively. The promise is that one reference state is the same as the unknown state and the task is to find out unambiguously which one it is. The particular choice of the reference states is unknown to us, and only the probability distribution describing this choice is known. In a general case when multiple copies of unknown and reference states are available I propose a scheme consisting of beamsplitters and photodetectors that is optimal within linear optics. UI can be considered as a search in a quantum database, whose elements are the reference states and the query is represented by the unknown state. This perspective motivated me to show that reference states can be recovered after the measurement and might be used (with reduced success rate) in subsequent UI. Moreover, I analyze the influence of noise in preparation of coherent states on the performance of the proposed setup. Another problem I address is the unambiguous comparison of a pair of unknown qudit unitary channels. I characterize all solutions and identify the optimal ones. I prove that in optimal experiments for comparison of unitary channels the entanglement is necessary. The last task I studied is the unambiguous comparison of unknown non-degenerate projective measurements. I distinguish between measurement devices with apriori labeled and unlabeled outcomes. In both cases only the difference of the measurements can be concluded unambiguously. For the labeled case I derive the optimal strategy if each unknown measurement is used only once. However, if the apparatuses are not labeled, then each measurement device must be used (at least) twice. In particular, for qubit measurement apparatuses with unlabeled outcomes I derive the optimal test state in the two-shots scenario.

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QUANTUM THEORY OF SPONTANEOUS SCATTERING OF LIGHT AND COHERENT STATES OF THREE-DIMENSIONAL LORENTZ GROUP

Vestnik of Samara University Natural Science Series ◽

10.18287/2541-7525-2011-17-2-171-178 ◽

2017 ◽

Vol 17 (2) ◽

pp. 171-178

Author(s):

A.V. Gorokhov ◽

D.I. Umov

Keyword(s):

Quantum Theory ◽

Lorentz Group ◽

Coherent States ◽

Nonlinear Optical ◽

Three Dimensional ◽

Scattering Of Light ◽

Optical Effects ◽

Nonlinear Optical Effects ◽

Parametric Down Conversion ◽

Down Conversion

The work is devoted to applications of group-theoretic coherent states todescribe the nonlinear optical effects. Important in modern quantum informationprocess of parametric down conversion is studied. It is shown that the useof superpositions of coherent states of SU(1; 1) allows to increase the squeezingof generated photon pairs.

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