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- Title
Propagation of correlations in local random quantum circuits.
- Authors
Santra, Siddhartha; Balu, Radhakrishnan
- Abstract
We derive a dynamical bound on the propagation of correlations in local random quantum circuits-lattice spin systems where piecewise quantum operations-in space and time-occur with classical probabilities. Correlations are quantified by the Frobenius norm of the commutator of two positive operators acting on disjoint regions of a one-dimensional circular chain of length L. For a time $$t=O(L)$$ , correlations spread ballistically to spatial distances $$\mathcal {D}=t$$ , growing at best, diffusively with time for any distance within that radius with extensively suppressed distance- dependent corrections. For $$t=\varOmega (L^2)$$ , all parts of the system get almost equally correlated with exponentially suppressed distance- dependent corrections and approach the maximum amount of correlations that may be established asymptotically.
- Subjects
QUANTUM operators; STATISTICAL correlation; COMMUTATORS (Operator theory); FROBENIUS groups; LATTICE theory
- Publication
Quantum Information Processing, 2016, Vol 15, Issue 11, p4613
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-016-1412-y