Energy-limited quantum dynamics
arXiv:2405.10259 · doi:10.1007/s00220-025-05282-w
Abstract
We consider quantum systems with energy constraints relative to a reference Hamiltonian. In general, quantum channels and continuous-time dynamics need not satisfy energy conservation. Physically meaningful channels, however, only introduce a finite amount of energy to the system, and continuous-time dynamics only increase the energy gradually over time. We systematically study such "energy-limited" channels and dynamics. For Markovian dynamics, energy-limitedness is equivalent to a single operator inequality in the Heisenberg picture. We observe new submultiplicativity inequalities for the energy-constrained diamond and operator norms and use them to derive new state-dependent continuity bounds for quantum speed limits.
Comments welcome
References in corpus (20)
- Advances in Quantum Cryptography
- Fundamental Limits of Repeaterless Quantum Communications
- General Benchmarks for Quantum Repeaters
- A Sharp Fannes-type Inequality for the von Neumann Entropy
- Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
- Energy-constrained diamond norms and their use in quantum information theory
- Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
- Unbounded generators of dynamical semigroups
- Enhanced energy-constrained quantum communication over bosonic Gaussian channels
- Energy-constrained two-way assisted private and quantum capacities of quantum channels
- Convergence rates for quantum evolution & entropic continuity bounds in infinite dimensions
- Strong Error Bounds for Trotter & Strang-Splittings and Their Implications for Quantum Chemistry
- Strong convergence of quantum channels: continuity of the Stinespring dilation and discontinuity of the unitary dilation
- State-dependent Trotter Limits and their approximations
- Entanglement-assisted capacity of constrained quantum channel
- Self-Adjointness of Toeplitz Operators on the Segal-Bargmann Space
- Extreme points of the set of quantum states with bounded energy
- Error bounds for Lie Group representations in quantum mechanics
- On Strong Bounds for Trotter and Zeno Product Formulas with Bosonic Applications
- Optimal form of the Kretschmann-Schlingemann-Werner theorem for energy-constrained quantum channels and operations