The Extension of Unital Completely Positive Semigroups on Operator Systems to Semigroups on $C^{\ast }$-algebras

Abstract

The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^{\ast }$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on operator systems. We show that any continuous unital completely positive semigroup on matricial system can be extended to a semigroup on a finite-dimensional $C^{\ast }$-algebra, which is an injective envelope of the matricial system. In case the semigroup is invertible, this extension is unique.

arXiv comment21 pages, 1 figure, typos corrected, journal reference added

References in corpus (11)

• Zero-error communication via quantum channels, non-commutative graphs and a quantum Lovasz theta function
• Operator system structures on ordered spaces
• A 2 rebit gate universal for quantum computing
• Spectrahedral Containment and Operator Systems with Finite-Dimensional Realization
• Unbounded generators of dynamical semigroups
• Entangleability of cones
• The noncommutative Choquet boundary III: Operator systems in matrix algebras
• Non-commutative graphs based on finite-infinite system couplings: quantum error correction for a qubit coupled to a coherent field
• On errors generated by unitary dynamics of bipartite quantum systems
• Unital Dilations of Completely Positive Semigroups: From Combinatorics to Continuity
• A short proof of the Arendt-Chernoff-Kato theorem

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