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Structure and Parametrization of Generic Stochastic Maps of Density Matrices

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E. C. G. Sudarshan, Anil Shaji

Quantum Physics · Submitted 9 May 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This is extended to all positive (not completely positive) maps.

how it is stated · asserted 0.97 read the record →

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arXiv IDquant-ph/0205051 (version 2)
Pith IDULU2BDZE, Pith's permanent record of this paper and its review
CitationAnil Shaji, E. C. G. Sudarshan. "Structure and Parametrization of Generic Stochastic Maps of Density Matrices." arXiv:quant-ph/0205051 (2002). https://pith.science/paper/ULU2BDZE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,070 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. The property of hermiticity of density matrices renders an associated supermatrix hermitian and hence diagonalizable. The positivity of the density matrix does not make the associated supermatrix positive though. If the map itself is positive, it is called completely positive and they have a simple parameterization. This is extended to all positive (not completely positive) maps. A general dynamical map that does not preserve the norm of the density matrices it acts on can be thought of as the contraction of a norm-preserving map of an extended system. The reconstruction of such extended dynamics is also given.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. background 1.00 0.09 0.12 asserted 1.00
s1 These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. background 0.74 0.24 0.08 hedged possibility 0.86
s2 The property of hermiticity of density matrices renders an associated supermatrix hermitian and hence diagonalizable. result 0.68 0.37 0.07 asserted 1.00
s3 The positivity of the density matrix does not make the associated supermatrix positive though. result 0.58 0.39 0.07 asserted 1.00
s4 If the map itself is positive, it is called completely positive and they have a simple parameterization. background 0.80 0.25 0.14 asserted 1.00
s5 This is extended to all positive (not completely positive) maps. contribution 0.92 0.76 0.19 asserted 0.97
s6 A general dynamical map that does not preserve the norm of the density matrices it acts on can be thought of as the contraction of a norm-preserving map of an extended system. contribution 0.32 0.40 0.11 hedged possibility 0.70
s7 The reconstruction of such extended dynamics is also given. contribution 0.77 0.79 0.11 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. The property of hermiticity of density matrices renders an associated supermatrix hermitian and hence diagonalizable. The positivity of the density matrix does not make the associated supermatrix positive though. If the map itself is positive, it is called completely positive and they have a simple parameterization. This is extended to all positive (not completely positive) maps. A general dynamical map that does not preserve the norm of the density matrices it acts on can be thought of as the contraction of a norm-preserving map of an extended system. The reconstruction of such extended dynamics is also given.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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