Quantum random walks and vanishing of the second Hochschild cohomology

Details Quantum random walks and vanishing of the second Hochschild cohomology Quantum random walks and vanishing of the second Hochschild cohomology

2007-04-13

arxiv.org/abs/0704.1755v1

Mathematics

Operator Algebras

Scientific paper

10.1007/s11005-008-0233-z

Given a conditionally completely positive map $\mathcal L$ on a unital $\ast$-algebra $\A$, we find an interesting connection between the second Hochschild cohomology of $\A$ with coefficients in the bimodule $E_{\mathcal L}=\B^a(\A \oplus M)$ of adjointable maps, where $M$ is the GNS bimodule of $\mathcal L$, and the possibility of constructing a quantum random walk (in the sense of \cite{AP,LP,L,KBS}) corresponding to $\mathcal L$.

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