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:1602.06942 · Linear Algebra and its Applications

Quantum f-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spaces

Dániel Virosztek

Published Mar 29, 2016• 8 citations
arXivHTMLPDF
DOI
10.1016/j.laa.2016.03.031

Related papers

Maps on density operators preserving quantum $$f$$ -divergences

Lajos Molnár, Gergő Nagy, Patrícia Szokol

Quantum Information Processing•Jan 25, 2013•20 citations

Rank in Matrix Analysis: On the Preservers of Maximally Entangled States and Fractional Minimal Rank

Benjamin Großmann

For Hilbert spaces X , Y, the set of maximally entangled states, MES X ,Y , is a set of rank-1 positive semidefinite operators over the space X ⊗ Y.In this thesis, we consider the problem of classifying the linear maps that take maximally entangled states to maximally entangled states in the case of finite dimensional spaces X , Y.After classifying these linear maps in the case where dim X divides dim Y, we consider possible avenues of extending these results and consider the set WMES X ,Y , which is a set of low-rank positive semidefinite operators over X ⊗ Y.We then discuss the "fractional minimal rank", a fractional parameter assigned to partial matrices.We compute the fractional minimal rank for partial matrices whose pattern of knowns is a "minimal cycle", which is the family of the smallest cases for which it is known that the "minimal rank" and "triangular minimal ranks" differ in general.

•Jan 1, 2019•0 citations

Entanglement preserving maps and the universality of finite time disentanglement

Raphael C. Drumond, Cristhiano Duarte, Marcelo Terra Cunha +1 more

In this paper we investigate how common is the phenomenon of Finite Time Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite quantum states with finite dimensional Hilbert spaces. Considering a quantum dynamics from a general sense, as just a continuous family of Completely Positive Trace Preserving maps (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD does not happen only when all maps of the family are induced by local unitary operations. We prove that is the case for dynamics where all maps are induced by unitaries and, for pairs of qubits, where all maps are unital. Moreover, we prove some results about unitaries/CPTP maps preserving product/pure states.

arXiv:1510.06466•Oct 22, 2015•0 citations

Transformations on density operators and on positive definite operators preserving the quantum Rényi divergence

Marcell Gaál, Lajos Molnár

arXiv:1512.02490•Periodica Mathematica Hungarica•Nov 10, 2016•1 citation

Jarzynski equality for quantum stochastic maps

Alexey E. Rastegin, Karol Życzkowski

Jarzynski equality and related fluctuation theorems can be formulated for various setups. Such an equality was recently derived for nonunitary quantum evolutions described by unital quantum operations, i.e., for completely positive, trace-preserving maps, which preserve the maximally mixed state. We analyze here a more general case of arbitrary quantum operations on finite systems and derive the corresponding form of the Jarzynski equality. It contains a correction term due to nonunitality of the quantum map. Bounds for the relative size of this correction term are established and they are applied for exemplary systems subjected to quantum channels acting on a finite-dimensional Hilbert space.

arXiv:1307.5370•Physical Review E•Jan 17, 2014•74 citations

Maps preserving a new version of quantum $f$ -divergence

Marcell Gaál

Banach Journal of Mathematical Analysis•Jun 22, 2017•2 citations
Maps on density operators preserving quantum fff -divergences
For Hilbert spaces X , Y, the set of maximally entangled states, MES X ,Y , is a set of rank-1 positive semidefinite operators over the space X ⊗ Y.In this thesis, we consider the problem of classifying the linear maps that take maximally entangled states to maximally entangled states in the case of finite dimensional spaces X , Y.After classifying these linear maps in the case where dim X divides dim Y, we consider possible avenues of extending these results and consider the set WMES X ,Y , which is a set of low-rank positive semidefinite operators over X ⊗ Y.We then discuss the "fractional minimal rank", a fractional parameter assigned to partial matrices.We compute the fractional minimal rank for partial matrices whose pattern of knowns is a "minimal cycle", which is the family of the smallest cases for which it is known that the "minimal rank" and "triangular minimal ranks" differ in general.
In this paper we investigate how common is the phenomenon of Finite Time Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite quantum states with finite dimensional Hilbert spaces. Considering a quantum dynamics from a general sense, as just a continuous family of Completely Positive Trace Preserving maps (parametrized by the time variable) acting on the space of the bipartite systems, we conjecture that FTD does not happen only when all maps of the family are induced by local unitary operations. We prove that is the case for dynamics where all maps are induced by unitaries and, for pairs of qubits, where all maps are unital. Moreover, we prove some results about unitaries/CPTP maps preserving product/pure states.
Jarzynski equality and related fluctuation theorems can be formulated for various setups. Such an equality was recently derived for nonunitary quantum evolutions described by unital quantum operations, i.e., for completely positive, trace-preserving maps, which preserve the maximally mixed state. We analyze here a more general case of arbitrary quantum operations on finite systems and derive the corresponding form of the Jarzynski equality. It contains a correction term due to nonunitality of the quantum map. Bounds for the relative size of this correction term are established and they are applied for exemplary systems subjected to quantum channels acting on a finite-dimensional Hilbert space.
Maps preserving a new version of quantum fff -divergence