Propagation of correlations in Local Random Quantum Circuits

Siddhartha Santra; Radhakrishnan Balu

doi:10.1007/s11128-016-1412-y

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arXiv · 1506.03323

Propagation of correlations in Local Random Quantum Circuits

Siddhartha Santra·Radhakrishnan Balu

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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 space-like separated local Hilbert spaces. For times $t=O(L)$ correlations spread to distances $\mathcal{D}=t$ growing, at best, diffusively for any distance within that radius with extensively suppressed distance dependent corrections whereas for $t=o(L^2)$ 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.

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BibTeX RIS

Siddhartha Santra, Radhakrishnan Balu. 2015-08-17. Propagation of correlations in Local Random Quantum Circuits. https://doi.org/10.1007/s11128-016-1412-y

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