Quantum and classical dynamical semigroups of superchannels and semicausal channels
arXiv:2109.03847 · doi:10.1063/5.0070635
Abstract
Quantum devices are subject to natural decay. We propose to study these decay processes as the Markovian evolution of quantum channels, which leads us to dynamical semigroups of superchannels. A superchannel is a linear map that maps quantum channels to quantum channels, while satisfying suitable consistency relations. If the input and output quantum channels act on the same space, then we can consider dynamical semigroups of superchannels. No useful constructive characterization of the generators of such semigroups is known. We characterize these generators in two ways: First, we give an efficiently checkable criterion for whether a given map generates a dynamical semigroup of superchannels. Second, we identify a normal form for the generators of semigroups of quantum superchannels, analogous to the GKLS form in the case of quantum channels. To derive the normal form, we exploit the relation between superchannels and semicausal completely positive maps, reducing the problem to finding a normal form for the generators of semigroups of semicausal completely positive maps. We derive a normal for these generators using a novel technique, which applies also to infinite-dimensional systems. Our work paves the way to a thorough investigation of semigroups of superchannels: Numerical studies become feasible because admissible generators can now be explicitly generated and checked. And analytic properties of the corresponding evolution equations are now accessible via our normal form.
arXiv comment33 pages, 6 figures; corrected some typos and updated the list of references
References in corpus (25)
- Quantum correlations with no causal order
- Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
- Assessing non-Markovian dynamics
- Quantum computations without definite causal structure
- Theoretical framework for quantum networks
- Quantum Circuits Architecture
- Transforming quantum operations: quantum supermaps
- Dividing Quantum Channels
- Quantum Channels with Memory
- Causal and localizable quantum operations
- Comparison of Quantum Channels by Superchannels
- Semicausal operations are semilocalizable
- Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
- On quantum non-signalling boxes
- Theoretical framework for Higher-Order Quantum Theory
- Extracting dynamical equations from experimental data is NP-hard
- Thermodynamic Capacity of Quantum Processes
- Entropy of a quantum channel
- Dynamics of quantum causal structures
- RTNI - A symbolic integrator for Haar-random tensor networks
- Entanglement-breaking superchannels
- The Complexity of Divisibility
- Normal completely positive maps on the space of quantum operations
- Revisiting dynamics of quantum causal structures -- when can causal order evolve?
- Necessary Criteria for Markovian Divisibility of Linear Maps