Quantum Information Scrambling Through a High-Complexity Operator Mapping
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Recently, quantum information scrambling has attracted much attention amid the effort to reconcile the apparent conflict between quantum-mechanical unitarity and the irreversibility of thermalizaiton in quantum many-body systems. Here we propose an unconventional mechanism to generate quantum information scrambling through a high-complexity mapping from logical to physical degrees of freedom that hides the logical information into non-separable many-body correlations. We develop an algorithm to compute all physical observables in dynamics with a polynomial-in-system-size cost. The system shows information scrambling in the quantum many-body Hilbert space characterized by the spreading of Hamming distance defined by a set of a natural orbital bases, which can also be calculated with a time polynomial in system size. Despite the polynomial complexity, the operator-mapping enabled growth in the out-of-time-order-correlator still exhibits quantum chaotic behavior. The information-hiding mapping approach opens up a novel venue to investigate fundamental connections among computational complexity, information scrambling and quantum thermalization.
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