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Probing the entanglement of operator growth. (English) Zbl 1502.81012

Summary: In this work we probe the operator growth for systems with Lie symmetry using tools from quantum information. Namely, we investigate the Krylov complexity, entanglement negativity, entanglement entropy, and capacity of entanglement for systems with SU(1,1) and SU(2) symmetry. Our main tools are two-mode coherent states, whose properties allow us to study the operator growth and its entanglement structure for any system in a discrete series representation of the groups under consideration. Our results verify that the quantities of interest exhibit certain universal features in agreement with the universal operator growth hypothesis. Moreover, we illustrate the utility of this approach relying on symmetry as it significantly facilitates the calculation of quantities probing operator growth. In particular, we argue that the use of the Lanczos algorithm, which has been the most important tool in the study of operator growth so far, can be circumvented and all the essential information can be extracted directly from symmetry arguments.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P40 Quantum coherence, entanglement, quantum correlations
81P42 Entanglement measures, concurrencies, separability criteria
68Q12 Quantum algorithms and complexity in the theory of computing
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
81R30 Coherent states
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