Quantum Supermaps are Characterized by Locality
Centre National de la Recherche Scientifique · King's College London · +7 more institutions
Abstract
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational probabilistic theories. We do so by providing a simple definition of locally-applicable transformation on a monoidal category. The definition can be rephrased in the language of category theory using the principle of naturality, and can be given an intuitive diagrammatic representation in terms of which all proofs are presented. In our main technical contribution, we use this diagrammatic representation to show that locally-applicable transformations on quantum channels are in…
Citation impact
- FWCI
- 24.35
- Percentile
- 98%
- References
- 73
Authors
3- MWMatt WilsonCorresponding
Centre National de la Recherche Scientifique, King's College London, Université Paris-Saclay, University of Oxford, CentraleSupélec, University College London, University of Hong Kong
- GCGiulio Chiribella
Perimeter Institute, University of Oxford, Centre for Quantum Computation and Communication Technology, University of Hong Kong
- AKAleks Kissinger
University of Oxford
Topics & keywords
- Diagrammatic reasoning
- Axiom
- Quantum
- Categorical quantum mechanics
- Mathematical proof
- Probabilistic logic
- Mathematics
- Representation (politics)