A note on the distributions in quantum mechanical systems

• URL: http://arxiv.org/abs/2104.05530v3
• Date: Tue, 20 Apr 2021 08:41:14 GMT
• Title: A note on the distributions in quantum mechanical systems
• Authors: Layth M. Alabdulsada
• Abstract summary: We study the distributions and the affine distributions of the quantum mechanical system. We discuss the controllability of the quantum mechanical system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we study the distributions and the affine distributions of the quantum mechanical system. Also, we discuss the controllability of the quantum mechanical system with the related question concerning the minimum time needed to steer a quantum system from a unitary evolution $U(0)=I$ of the unitary propagator to a desired unitary propagator $U_f$. Furthermore, the paper introduces a description of a $\mathfrak{k} \oplus \mathfrak{p}$ sub-Finsler manifold with its geodesics, which equivalents to the problem of driving the quantum mechanical system from an arbitrary initial state $U(0)=I$ to the target state $U_f$, some illustrative examples are included. We prove that the Lie group $G$ on a Finsler symmetric manifold $G/K$ can be decomposed into $KAK$.

Related papers

• Quantum model for black holes and clocks [41.99844472131922]
  We consider a stationary quantum system consisting of two non-interacting yet entangled subsystems, $$ and $$.<n>We identify a quantum theory characterizing $$ such that, in the quantum-to-classical crossover of the composite system, $$ behaves as a test particle within the gravitational field of a Schwarzschild Black Hole.<n>This leads us to discuss how the quantum model for $$ endows the SBH with all the characteristics of a "perfect" clock.
  arXiv  Detail & Related papers  (2026-01-12T11:26:06Z)
• Open Quantum Systems as Regular Holonomic $\mathcal{D}$-Modules: The Mixed Hodge Structure of Spectral Singularities [0.0]
  We show that the open quantum system underlies a textbf Hodge Module structure in the sense of Saito.<n>This identification allows us to apply the textbfGrothendieck six-functor formalism rigorously to dissipative dynamics.
  arXiv  Detail & Related papers  (2025-12-22T15:43:35Z)
• Freeness Reined in by a Single Qubit [36.94429692322632]
  We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$.<n>We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.
  arXiv  Detail & Related papers  (2025-12-15T19:00:09Z)
• Exact Relation Between Wehrl-Rényi Entropy and Many-Body Entanglement [13.703543201381892]
  We establish an exact relation between the Wehrl-R'enyi entropy (WRE) $S_W(2)$, which is the 2nd R'enyi entropy of the Husimi function of the entire system.<n>We analytically derive the WRE for several representative many-body states, including Haar-random states, the Greenberger-Horne-Zeilinger (GHZ) state, and the W state.
  arXiv  Detail & Related papers  (2025-09-19T14:43:58Z)
• Quantum Tomography in Neutral Meson and Antimeson Systems [4.715411959818119]
  We present a systematic approach for constructing the complete flavor density matrix for a meson and antimeson system ($M bar M$) in the Bloch vector space at a given time $t$.<n> Performing quantum tomography for the $M bar M$ system can facilitate the study of production mechanisms, decoherence phenomena, quantum information variables, and potential new sources of CP violation.
  arXiv  Detail & Related papers  (2025-07-16T18:00:00Z)
• Commutators with multiple unitary symmetry [8.572991879638712]
  Commutators are essential in quantum information theory, influencing quantum state symmetries and information storage robustness. This paper systematically investigates the characteristics of bipartite and multipartite quantum states invariant under local unitary group actions.
  arXiv  Detail & Related papers  (2025-04-12T14:16:23Z)
• Packaged Quantum States and Symmetry: A Group-Theoretic Approach to Gauge-Invariant Packaged Entanglements [0.0]
  A packaged quantum state refers to a quantum state that includes an inseparable block of internal quantum numbers. We show that in multiparticle quantum systems, any nontrivial representation of a finite or compact group induces packaged entanglement. The results may be useful for applications in exotic hadron spectroscopy, extended symmetries in quantum field theory, and quantum technologies.
  arXiv  Detail & Related papers  (2025-03-26T07:35:58Z)
• Approximation of diffeomorphisms for quantum state transfers [49.1574468325115]
  We seek to combine two emerging standpoints in control theory. We numerically find control laws driving state transitions in a bilinear Schr"odinger PDE posed on the torus.
  arXiv  Detail & Related papers  (2025-03-18T17:28:59Z)
• PT-Symmetric $SU(2)$-like Random Matrix Ensembles: Invariant Distributions and Spectral Fluctuations [0.0]
  The randomness of the ensemble is endowed by obtaining probability distributions based on symmetry and statistical independence. The degree of level repulsion is a parameter of great interest as it makes a connection to quantum chaos.
  arXiv  Detail & Related papers  (2025-01-11T17:34:09Z)
• Symmetry: a fundamental resource for quantum coherence and metrology [0.0]
  We show that when the quantum state is an eigenstate of an operator $A$, observables $G$ which are completely off-diagonal have purely quantum fluctuations. This property holds regardless of the purity of the quantum state, and it implies that off-diagonal fluctuations represent a metrological resource for phase estimation.
  arXiv  Detail & Related papers  (2024-07-01T07:19:37Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• Rigorous Bounds on Eigenstate Thermalization [4.511923587827301]
  Eigenstate thermalization hypothesis (ETH) asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble. No evidence has been obtained as to whether the ETH holds for $textitany$ few-body operators in a chaotic system.
  arXiv  Detail & Related papers  (2023-03-17T15:52:08Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• On quantum tomography on locally compact groups [0.0]
  We introduce quantum tomography on locally compact Abelian groups $G$. We provide three examples in which $G=mathbb R$ (the optical tomography), $G=mathbb Z_n$ (corresponding to measurements in mutually unbiased bases) and $G=mathbb T$ (the tomography of the phase) As an application we have calculated the quantum tomogram for the output states of quantum Weyl channels.
  arXiv  Detail & Related papers  (2022-01-16T13:48:22Z)
• On quantum algorithms for the Schr\"odinger equation in the semi-classical regime [27.175719898694073]
  We consider Schr"odinger's equation in the semi-classical regime. Such a Schr"odinger equation finds many applications, including in Born-Oppenheimer molecular dynamics and Ehrenfest dynamics.
  arXiv  Detail & Related papers  (2021-12-25T20:01:54Z)
• Straddling-gates problem in multipartite quantum systems [20.428960719376164]
  We study a variant of quantum circuit complexity, the binding complexity. We show that any $m$partite Schmidt decomposable state has binding complexity linear in $m$, which hints its multi-separable property.
  arXiv  Detail & Related papers  (2021-10-13T16:28:12Z)
• Symmetric distinguishability as a quantum resource [21.071072991369824]
  We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources. We study the resource theory for two different classes of free operations: $(i)$ $rmCPTP_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly (CDS) maps acting on $XA$.
  arXiv  Detail & Related papers  (2021-02-24T19:05:02Z)
• Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions [0.0]
  We show how the entanglement splits between the sectors of an internal local symmetry of a quantum many-body system. We point out two physically relevant effects that should be easily observed in atomic experiments.
  arXiv  Detail & Related papers  (2020-10-19T19:12:42Z)
• Spectral statistics in constrained many-body quantum chaotic systems [0.0]
  We study the spectral statistics of spatially-extended many-body quantum systems with on-site Abelian symmetries or local constraints. In particular, we analytically argue that in a system of length $L$ that conserves the $mth$ multipole moment, $t_mathrmTh$ scales subdiffusively as $L2(m+1)$.
  arXiv  Detail & Related papers  (2020-09-24T17:59:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.