Final published version
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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 - Quasifree Stochastic Cocycles and Quantum Random Walks
AU - Belton, Alexander Charles Richard
AU - Gnacik, Michal
AU - Lindsay, Jonathan Martin
AU - Zhong, Ping
PY - 2019/7/15
Y1 - 2019/7/15
N2 - The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson–Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed, and related to the minimality of the corresponding stochastic dilation. The theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises.
AB - The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson–Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect to which a given unitary quantum stochastic cocycle is quasifree is addressed, and related to the minimality of the corresponding stochastic dilation. The theory is applied to the identification of a wide class of quantum random walks whose limit processes are driven by quasifree noises.
KW - Quantum stochastic calculus
KW - Quasifree representation
KW - Heat bath
KW - Repeated quantum interactions
KW - Noncommutative Markov chain
KW - Quantum Langevin equation
U2 - 10.1007/s10955-019-02273-9
DO - 10.1007/s10955-019-02273-9
M3 - Journal article
VL - 176
SP - 1
EP - 39
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 1
ER -