Almost All Quantum Channels Are Diagonalizable
arXiv:2403.19643 · doi:10.1142/S1230161224500124
Abstract
We prove the statement "The collection of all elements of which have only simple eigenvalues is dense in " for different sets , including: all quantum channels, the unital channels, the positive trace-preserving maps, all Lindbladians (GKSL-generators), and all time-dependent Markovian channels. Therefore any element from each of these sets can always be approximated by diagonalizable elements of the same set to arbitrary precision.
arXiv comment11+3 pages
References in corpus (23)
- The physics of exceptional points
- Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
- Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
- Dividing Quantum Channels
- Adiabatic approximation in open quantum systems
- A general framework for randomized benchmarking
- Information preserving structures: A general framework for quantum zero-error information
- Adiabaticity in open quantum systems
- Ergodic and Mixing Quantum Channels in Finite Dimensions
- Abelian and non-Abelian geometric phases in adiabatic open quantum systems
- Heat-Bath Algorithmic Cooling with optimal thermalization strategies
- Markovian evolution of quantum coherence under symmetric dynamics
- Information flow versus divisibility for qubit evolution
- Divisibility of qubit channels and dynamical maps
- Asymptotic Evolution of Random Unitary Operations
- Open system dynamics from thermodynamic compatibility
- Fitting quantum noise models to tomography data
- Thermal Processes and State Achievability
- Which Bath-Hamiltonians Matter for Thermal Operations?
- Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources
- Construction of propagators for divisible dynamical maps
- Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics
- The Thermomajorization Polytope and Its Degeneracies