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Related papers: Complexity Growth and the Krylov-Wigner function

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We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans…

High Energy Physics - Theory · Physics 2025-06-19 Kyoung-Bum Huh , Hyun-Sik Jeong , Leopoldo A. Pando Zayas , Juan F. Pedraza

Measurement incompatibility and the negativity of quasiprobability distribution functions are well-known non-classical aspects of quantum systems. Both of them are widely accepted resources in quantum information processing. We acquaint an…

Quantum Physics · Physics 2023-06-14 Jatin Ghai , Gautam Sharma , Sibasish Ghosh

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of…

Quantum Physics · Physics 2009-11-10 J. G. Wood , A. J. Bracken

The exact solution of the Lindblad equation with a quadratic Hamiltonian and linear coupling operators was derived within the chord representation, that is, for the Fourier transform of the Wigner function, also known as the characteristic…

Quantum Physics · Physics 2023-10-04 Aldo R. Fernandes Neto , Alfredo M. Ozorio de Almeida , Olivier Brodier

The Wigner function plays a central role in QCD as a phase space object encoding correlations among quarks, antiquarks, and gluons, yet its interpretation remains subtle due to its quasiprobabilistic nature and possible negativity. Recent…

High Energy Physics - Phenomenology · Physics 2026-04-07 Chueng-Ryong Ji , Daniel W. Piasecki

In this work, we propose a quantum-mechanically measurable basis for the computation of spread complexity. Current literature focuses on computing different powers of the Hamiltonian to construct a basis for the Krylov state space and the…

Quantum Physics · Physics 2024-11-05 Saud Čindrak , Adrian Paschke , Lina Jaurigue , Kathy Lüdge

Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger…

General Relativity and Quantum Cosmology · Physics 2014-11-17 Julien Lesgourgues , David Polarski , Alexei A. Starobinsky

Quantifying complexity in quantum systems has witnessed a surge of interest in recent years, with Krylov-based measures such as Krylov complexity ($C_K$) and Spread complexity ($C_S$) gaining prominence. In this study, we investigate their…

High Energy Physics - Theory · Physics 2024-06-10 Pawel Caputa , Hyun-Sik Jeong , Sinong Liu , Juan F. Pedraza , Le-Chen Qu

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum state tomography. We theoretically propose and experimentally…

We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor…

High Energy Physics - Theory · Physics 2021-05-19 Jinn-Ouk Gong , Min-Seok Seo

The Wigner function's behavior of accelerated and non-accelerated Greenberger Horne Zeilinger (GHZ) state is discussed. For the non-accelerated GHZ state, the minimum/maximum peaks of the Wigner function depends on the distribution's…

Quantum Physics · Physics 2019-01-28 N. Metwally , M. Y. Abd Rabbou , M. M. A. Ahmed , A. S. F. Obada

We show that qubit stabilizer states can be represented by non-negative quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by…

Quantum Physics · Physics 2018-01-03 Lucas Kocia , Peter Love

A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…

Quantum Physics · Physics 2009-11-11 Arthur O. Pittenger , Morton H. Rubin

The Wigner function is known to evolve classically under the exclusive action of a quadratic hamiltonian. If the system does interact with the environment through Lindblad operators that are linear functions of position and momentum, we…

Quantum Physics · Physics 2009-11-10 O. Brodier , A. M. Ozorio de Almeida

Krylov complexity (K-complexity) is a measure of quantum state complexity that minimizes wavefunction spreading across all the possible bases. It serves as a key indicator of operator growth and quantum chaos. In this work, K-complexity and…

Quantum Physics · Physics 2025-10-08 J. Bharathi Kannan , Sreeram PG , Sanku Paul , S. Harshini Tekur , M. S. Santhanam

Wigner-positive quantum states have the peculiarity to admit a Wigner function that is a genuine probability distribution over phase space. The Shannon differential entropy of the Wigner function of such states -- called Wigner entropy for…

Quantum Physics · Physics 2026-01-27 Zacharie Van Herstraeten , Nicolas J. Cerf

A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…

Quantum Physics · Physics 2026-05-08 Surachate Limkumnerd , Panat Phanthaphanitkul

The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…

Quantum Physics · Physics 2009-11-10 Kathleen S. Gibbons , Matthew J. Hoffman , William K. Wootters

Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time…

High Energy Physics - Theory · Physics 2021-10-04 Anatoly Dymarsky , Michael Smolkin

We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name…

Quantum Physics · Physics 2022-01-03 Zacharie Van Herstraeten , Nicolas J. Cerf