Positive-Operator Valued Measure (POVM) Quantization

Gazeau, Jean Pierre; Heller, Bárbara

doi:10.3390/axioms4010001

Cited by 23 publications

(14 citation statements)

References 30 publications

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“…The eigenvalues of H ph form the 'quantum spectrum' of a classical observable f whereas its 'classical spectrum' coincides with the set of values {E n = f (a n )} N n=1 [12,13]. These results can be generalized to the case of infinite Parseval frames with the use of POVM quantization developed in [15].…”

Section: Introductionmentioning

confidence: 94%

Hamiltonians Generated by Parseval Frames

Багарелло

Kużel

2020

Acta Appl Math

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It is known that self-adjoint Hamiltonians with purely discrete eigenvalues can be written as (infinite) linear combination of mutually orthogonal projectors with eigenvalues as coefficients of the expansion. The projectors are defined by the eigenvectors of the Hamiltonians. In some recent papers, this expansion has been extended to the case in which these eigenvectors form a Riesz basis or, more recently, a ${\mathcal{D}}$ D -quasi basis (Bagarello and Bellomonte in J. Phys. A 50:145203, 2017, Bagarello et al. in J. Math. Phys. 59:033506, 2018), rather than an orthonormal basis. Here we discuss what can be done when these sets are replaced by Parseval frames. This interest is motivated by physical reasons, and in particular by the fact that the mathematical Hilbert space where the physical system is originally defined, contains sometimes also states which cannot really be occupied by the physical system itself. In particular, we show what changes in the spectrum of the observables, when going from orthonormal bases to Parseval frames. In this perspective we propose the notion of $E$ E -connection for observables. Several examples are discussed.

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Section: Introductionmentioning

confidence: 94%

Hamiltonians Generated by Parseval Frames

Багарелло

Kużel

2020

Acta Appl Math

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“…We have k matrices means that we must have k outcomes. So, probability of coming any i th outcome is given by [17]…”

Section: Trace Distancementioning

confidence: 99%

Quantum Cryptography–A Theoretical Overview

Roy¹,

Sahoo²,

Mandal³

et al. 2021

Journal of Quantum Computing

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Quantum Key Distribution seems very promising as it offers unconditional security, that's why it is being implemented by the tech giants of the networking industry and government. Having quantum phenomenon as a backbone, QKD protocols become indecipherable. Here we have focused on the complexities of quantum key distribution and how this technology has contributed to secure key communication. This article gives an updated overview of this technology and can serve as a guide to get familiar with the current trends of quantum cryptography.

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“…Integral quantization [9,10,11,12,13,14,15,16] is a generic name of approaches to quantization based on operator-valued measures. It includes the so-called Berezin-Klauder-Toeplitz quantization, and more specifically coherent state quantization [10,17].…”

Section: Integral Quantizationmentioning

confidence: 99%

Quantum Mixmaster as a Model of the Primordial Universe

et al. 2019

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The Mixmaster solution to Einstein field equations was examined by C. Misner in an effort to better understand the dynamics of the early universe. We highlight the importance of the quantum version of this model for early universe. This quantum version and its semi-classical portraits are yielded through affine and standard coherent state quantizations and more generally affine and Weyl-Heisenberg covariant integral quantizations. The adiabatic and vibronic approximations widely used in molecular physics can be employed to qualitatively study the dynamics of the model on both quantum and semi-classical levels. Moreover, the semi-classical approach with the exact anisotropy potential can be effective in numerical integration of some solutions. Some promising physical features such as the singularity resolution, smooth bouncing, the excitation of anisotropic oscillations and a substantial amount of post-bounce inflation as the backreaction to the latter are pointed out. Finally, a realistic cosmological scenario based on the quantum mixmaster model, which includes the formation and evolution of local structures is outlined.

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Positive-Operator Valued Measure (POVM) Quantization

Cited by 23 publications

References 30 publications

Hamiltonians Generated by Parseval Frames

Hamiltonians Generated by Parseval Frames

Quantum Cryptography–A Theoretical Overview

Quantum Mixmaster as a Model of the Primordial Universe

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