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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Strong convergence of quantum random walks via semigroup decomposition
AU - Belton, Alexander Charles Richard
AU - Gnacik, Michal
AU - Lindsay, Jonathan Martin
N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s00023-018-0676-4
PY - 2018/6
Y1 - 2018/6
N2 - We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise product of quantum random walks to the quantum stochastic Trotter product of the respective limit cocycles, thereby revealing the algebraic structure of the limiting procedure. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described.
AB - We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise product of quantum random walks to the quantum stochastic Trotter product of the respective limit cocycles, thereby revealing the algebraic structure of the limiting procedure. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described.
KW - Quantum random walk
KW - repeated interactions
KW - noncommutative Markov chain
KW - toy Fock space
KW - quantum stochastic cocycle
KW - series product
KW - quantum stochastic Trotter product
U2 - 10.1007/s00023-018-0676-4
DO - 10.1007/s00023-018-0676-4
M3 - Journal article
VL - 19
SP - 1711
EP - 1746
JO - Annales Henri Poincaré
JF - Annales Henri Poincaré
SN - 1424-0637
IS - 6
ER -