Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States
arXiv (Cornell University)(2023)
摘要
Entanglement properties of purified quantum states are of key interest for
two reasons. First, in quantum information theory, minimally entangled purified
states define the Entanglement of Purification as a fundamental measure for the
complexity of the corresponding physical mixed state. Second, dynamical
entanglement growth in purified states represents the main bottleneck for
calculating dynamical physical properties on classical computers in the
framework of tensor network states. Here, we demonstrate how geometric methods
including parallel transport may be harnessed to reduce such dynamical
entanglement growth, and to obtain a general prescription for maintaining
(locally) optimal entanglement entropy when time-evolving a purified state.
Adapting and extending by higher order skew corrections the notion of Uhlmann
geometric phases, we reveal the relation between dynamical entanglement growth
and the geometry of the Hilbert-Schmidt bundle as the mathematical foundation
of purified states. With benchmarks on a non-integrable spin chain model, we
compare the computational performance of matrix product state algorithms based
on our present geometric disentangling method to previous approaches for taming
entanglement growth in purified states. Our findings provide numerical evidence
that geometric disentanglers are a powerful approach for disentangling purified
states in an extended physical parameter regime. To exclude the effect of
algorithmic imperfections, we also provide a numerically exact analysis for
systems of moderate size.
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关键词
purified quantum
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