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

Foundations of Physics

Another look at complete positivity in generalized quantum dynamics: Reply to Raggio and Primas

Ralph F. Simmons, James L Park

Published Apr 1, 1982• 9 citations
Publisher
DOI
10.1007/bf00726788

Related papers

Remarks on ?On Completely Positive Maps in Generalized Quantum Dynamics?

G. A. Raggio, Hans Primas

Foundations of Physics•Apr 1, 1982•15 citations

On completely positive maps in generalized quantum dynamics

Ralph F. Simmons, James L Park

Foundations of Physics•Feb 1, 1981•17 citations

Complete Positivity in Dissipative Quantum Dynamics

Fabio Benatti, Roberto Floreanini B, R. Romano

Lecture notes in physics•Jan 1, 2002•1 citation

The EPR Problem and Nonseparability

Bernard d’Espagnat

This chapter temporarily departs from conventional "orthodoxy" in that the authors set aside the completeness hypothesis and its generalizations. In 1935 A. Einstein and his two younger collaborators, B. Podolsky and N. Rosen (EPR) issued a paper in which they showed that, assuming the validity of but very general and highly plausible assumptions, the incompleteness of quantum mechanics could be demonstrated. The opinion that quantum mechanics is a complete description of the atomic and subatomic phenomena was so much engrained in the mind of the physicists that this EPR result was soon referred to as a "paradox." The EPR argument was based on assumptions, or premises, that, prima facie look most plausible. On the theoretical side it has been shown that the D. Greenberger, M. Home, and A. Zeilinger argument can be developed without involving any spin, essentially by replacing the spin-component measurements by presence measurements performed by means of counters.

CRC Press eBooks•May 4, 2018•0 citations

Divisibility of Non-Invertible Quantum Dynamics in the Heisenberg Picture

Federico Settimo, Dariusz Chruściński

We study divisibility of finite-dimensional quantum dynamics in the Heisenberg picture when the dynamical maps need not be invertible. Heisenberg divisible dynamics determines unique reduced propagators on the accessible operator systems, and Heisenberg CP-divisibility is shown to be equivalent to an operator-norm monotonicity. Although each reduced propagator admits a unital completely positive extension, independently chosen extensions need not satisfy a composition law. Generalized inverses restore this law algebraically, but do not, in general, preserve complete positivity. We characterize the resulting obstruction and give a sufficient construction based on unital completely positive projections onto the accessible operator systems. It is shown that for qubit dynamics Heisenberg CP-divisibility always guarantees a completely positive generalized-inverse propagator. Finally, we analyze time-local generators at singular times and identify the associated gauge freedom on dynamically inaccessible directions.

quant-pharXiv:2610.07986•Oct 7, 2026•0 citations

Complete positivity, positivity, and long-time asymptotic behavior in a two-level open quantum system

Guillaume Théret, Dominique Sugny

We study the concepts of complete positivity and positivity in a two-level open quantum system whose dynamics are governed by a time-local quantum master equation. We establish necessary and sufficient conditions on the time-dependent relaxation rates to ensure complete positivity and positivity of the dynamical map. We discuss their relations with the non-Markovian behavior of the open system. We also analyze the long-time asymptotic behavior of the dynamics as a function of the rates. We show under which conditions on the rates the system tends to an equilibrium state. Different examples illustrate this general study.

arXiv:2304.01748•Physical Review A•Sep 18, 2023•5 citations
This chapter temporarily departs from conventional "orthodoxy" in that the authors set aside the completeness hypothesis and its generalizations. In 1935 A. Einstein and his two younger collaborators, B. Podolsky and N. Rosen (EPR) issued a paper in which they showed that, assuming the validity of but very general and highly plausible assumptions, the incompleteness of quantum mechanics could be demonstrated. The opinion that quantum mechanics is a complete description of the atomic and subatomic phenomena was so much engrained in the mind of the physicists that this EPR result was soon referred to as a "paradox." The EPR argument was based on assumptions, or premises, that, prima facie look most plausible. On the theoretical side it has been shown that the D. Greenberger, M. Home, and A. Zeilinger argument can be developed without involving any spin, essentially by replacing the spin-component measurements by presence measurements performed by means of counters.
We study divisibility of finite-dimensional quantum dynamics in the Heisenberg picture when the dynamical maps need not be invertible. Heisenberg divisible dynamics determines unique reduced propagators on the accessible operator systems, and Heisenberg CP-divisibility is shown to be equivalent to an operator-norm monotonicity. Although each reduced propagator admits a unital completely positive extension, independently chosen extensions need not satisfy a composition law. Generalized inverses restore this law algebraically, but do not, in general, preserve complete positivity. We characterize the resulting obstruction and give a sufficient construction based on unital completely positive projections onto the accessible operator systems. It is shown that for qubit dynamics Heisenberg CP-divisibility always guarantees a completely positive generalized-inverse propagator. Finally, we analyze time-local generators at singular times and identify the associated gauge freedom on dynamically inaccessible directions.
We study the concepts of complete positivity and positivity in a two-level open quantum system whose dynamics are governed by a time-local quantum master equation. We establish necessary and sufficient conditions on the time-dependent relaxation rates to ensure complete positivity and positivity of the dynamical map. We discuss their relations with the non-Markovian behavior of the open system. We also analyze the long-time asymptotic behavior of the dynamics as a function of the rates. We show under which conditions on the rates the system tends to an equilibrium state. Different examples illustrate this general study.