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arXiv · 0704.1755

Quantum random walks and vanishing of the second Hochschild cohomology

Debashish Goswami·Lingaraj Sahu
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Abstract

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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Debashish Goswami, Lingaraj Sahu. 2007-04-13. Quantum random walks and vanishing of the second Hochschild cohomology. https://doi.org/10.1007/s11005-008-0233-z

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