Details
| Original language | English |
|---|---|
| Pages (from-to) | 372-378 |
| Number of pages | 7 |
| Journal | J. Comput. Syst. Sci. |
| Volume | 77 |
| Publication status | Published - 2011 |
Abstract
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: J. Comput. Syst. Sci., Vol. 77, 2011, p. 372-378.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Unitarity plus causality implies localizability
AU - Arrighi, Pablo
AU - Nesme, Vincent
AU - Werner, Reinhard F.
PY - 2011
Y1 - 2011
N2 - We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution U. We require that this global evolution U be unitary, in accordance with quantum theory, and that this global evolution U be causal, in accordance with special relativity. By causal we mean that information can only ever be transmitted at a bounded speed, the speed bound being quite naturally that of one edge of the underlying graph per iteration of U. We show that under these conditions the operator U can be implemented locally; i.e. it can be put into the form of a quantum circuit made up with more elementary operators -- each acting solely upon neighbouring nodes. We apply this representation theorem to n-dimensional quantum cellular automata and show that they can be put into the form of an infinite tiling of more elementary, finite-dimensional unitary evolutions.
AB - We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution U. We require that this global evolution U be unitary, in accordance with quantum theory, and that this global evolution U be causal, in accordance with special relativity. By causal we mean that information can only ever be transmitted at a bounded speed, the speed bound being quite naturally that of one edge of the underlying graph per iteration of U. We show that under these conditions the operator U can be implemented locally; i.e. it can be put into the form of a quantum circuit made up with more elementary operators -- each acting solely upon neighbouring nodes. We apply this representation theorem to n-dimensional quantum cellular automata and show that they can be put into the form of an infinite tiling of more elementary, finite-dimensional unitary evolutions.
M3 - Article
VL - 77
SP - 372
EP - 378
JO - J. Comput. Syst. Sci.
JF - J. Comput. Syst. Sci.
SN - 1090-2724
ER -