Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2107.06874 · The Teaching of Mathematics

Gaussian integrals depending on a quantum parameter in finite dimension

Simone Camosso

Published Jan 1, 2022• 0 citations
arXivHTMLPDF

Abstract

A common theme in mathematics is the evaluation of Gauss integrals. This, coupled with the fact that they are used in different branches of science, makes the topic always actual and interesting. In these notes we shall analyze a particular class of Gaussian integrals that depends by the quantum parameter $\hbar$. Starting from classical results, we will present an overview on methods, examples and analogies regarding the practice of solving quantum Gaussian integrals.

DOI
10.57016/tm-zovb7625

Related papers

Quantum Stochastic Processes

Joseph Spring, Alexander I. Lvovsky

We consider quantum analogues of n‐parameter stochastic processes, associated integrals and martingale properties extending classical results obtained in [1, 2, 3], and quantum results in [4, 5, 6, 7, 8, 9, 10].

AIP conference proceedings•Jan 1, 2009•2 citations

Investigating student interpretations of the differences between classical and quantum computers: Are quantum computers just analog classical computers?

Josephine C. Meyer, Gina Passante, Steven J. Pollock +1 more

Significant attention in the PER community has been paid to student cognition and reasoning processes in undergraduate quantum mechanics.Until recently, however, these same topics have remained largely unexplored in the context of emerging interdisciplinary quantum information science (QIS) courses.We conducted exploratory interviews with 22 students in an upper-division quantum computing course at a large R1 university crosslisted in physics and computer science, as well as 6 graduate students in a similar graduate-level QIS course offered in physics.We classify and analyze students' responses to a pair of questions regarding the fundamental differences between classical and quantum computers.We specifically note two key themes of importance to educators: (1) when reasoning about computational power, students often struggled to distinguish between the relative effects of exponential and linear scaling, resulting in students frequently focusing on distinctions that are arguably better understood as analog-digital than classical-quantum, and (2) introducing the thought experiment of analog classical computers was a powerful tool for helping students develop a more expertlike perspective on the differences between classical and quantum computers.

arXiv:2208.13734•Physics Education Research Conference (PERC)•Sep 21, 2022•3 citations

Quantum Game: A New Boundary Economic Thoery

Chen Shou

Game theory is a very useful and important branch of mathematics,as it can solve many problems in economics,social science and biology.Quantum games and quantum strategies are a new born field,by giving a formal quantum structure to the usual mathematical tools commonly used in analyzing decision making problems.Extension of game theory to quantum domain leads to some interesting new results in addition to the resolution of some existing dilemmas in the classical versions of games.

Caijing lilun yu shijian•Jan 1, 2006•0 citations

Frequently Used Integrals in Quantum Mechanics

Yan Li

.This paper introduces the definition and calculating nature of two integral frequently used in Quantum Mechanics,and presents the methods and formularized results of Quantum Mechanics by using integral.

Journal of Yili Normal University•Jan 1, 2007•0 citations

The Quantum Agreement Theorem

María García Díaz, Adam Brandenburger, Giannicola Scarpa

Intersubjective consistency asks when different observers of a physical system, reasoning from a shared theory, will agree on their probability assessments. Classical probability theory provides a benchmark in the form of the Agreement Theorem (Aumann, 1976). We study the quantum mechanics (QM) analog to the classical Agreement Theorem in a finite-dimensional tripartite setting in which two observers obtain information via local projective measurements. We represent their mutual awareness by common certainty, which is formally an infinite hierarchy of certainty operators concerning the probability of an event of interest. We first prove that if the observers' measurements commute with one another and with the property of interest, common certainty forces their probability assessments to coincide, thereby recovering a QM analog to the classical Agreement Theorem. We then construct a one-parameter family of qutrit-qubit-qubit models in which one observer's measurement does not commute with the property and common certainty of disagreement occurs -- a distinctively QM phenomenon. The mechanism is coherence between branches distinguished by one but not the other observer's measurement. When measurement outcomes are stored in a classical register, the resulting dephasing removes this coherence and restores agreement. Finally, we prove that QM does not permit the extreme 0-1 configuration in which Alice is certain of a property and is also certain that Bob is certain of its negation. These results aim to turn debate in QM about observer-dependent facts into precise mathematical conditions for when intersubjective agreement or disagreement in QM can be sustained.

quant-pharXiv:2511.21258•Nov 27, 2025•0 citations

Generalized integrals of density matrices and Green's functions

Andreou, V., Jannussis, A., Goudaroulis, G.

In this paper we calculate generalized integrals density matrices which are expressed in terms or the canonical Bloch matrices and the Green's functions.

•Jan 1, 1977•0 citations
A common theme in mathematics is the evaluation of Gauss integrals. This, coupled with the fact that they are used in different branches of science, makes the topic always actual and interesting. In these notes we shall analyze a particular class of Gaussian integrals that depends by the quantum parameter ℏ\hbarℏ. Starting from classical results, we will present an overview on methods, examples and analogies regarding the practice of solving quantum Gaussian integrals.
Significant attention in the PER community has been paid to student cognition and reasoning processes in undergraduate quantum mechanics.Until recently, however, these same topics have remained largely unexplored in the context of emerging interdisciplinary quantum information science (QIS) courses.We conducted exploratory interviews with 22 students in an upper-division quantum computing course at a large R1 university crosslisted in physics and computer science, as well as 6 graduate students in a similar graduate-level QIS course offered in physics.We classify and analyze students' responses to a pair of questions regarding the fundamental differences between classical and quantum computers.We specifically note two key themes of importance to educators: (1) when reasoning about computational power, students often struggled to distinguish between the relative effects of exponential and linear scaling, resulting in students frequently focusing on distinctions that are arguably better understood as analog-digital than classical-quantum, and (2) introducing the thought experiment of analog classical computers was a powerful tool for helping students develop a more expertlike perspective on the differences between classical and quantum computers.
Intersubjective consistency asks when different observers of a physical system, reasoning from a shared theory, will agree on their probability assessments. Classical probability theory provides a benchmark in the form of the Agreement Theorem (Aumann, 1976). We study the quantum mechanics (QM) analog to the classical Agreement Theorem in a finite-dimensional tripartite setting in which two observers obtain information via local projective measurements. We represent their mutual awareness by common certainty, which is formally an infinite hierarchy of certainty operators concerning the probability of an event of interest. We first prove that if the observers' measurements commute with one another and with the property of interest, common certainty forces their probability assessments to coincide, thereby recovering a QM analog to the classical Agreement Theorem. We then construct a one-parameter family of qutrit-qubit-qubit models in which one observer's measurement does not commute with the property and common certainty of disagreement occurs -- a distinctively QM phenomenon. The mechanism is coherence between branches distinguished by one but not the other observer's measurement. When measurement outcomes are stored in a classical register, the resulting dephasing removes this coherence and restores agreement. Finally, we prove that QM does not permit the extreme 0-1 configuration in which Alice is certain of a property and is also certain that Bob is certain of its negation. These results aim to turn debate in QM about observer-dependent facts into precise mathematical conditions for when intersubjective agreement or disagreement in QM can be sustained.