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Studying the relations between entanglement and coherence is essential inmany quantum information applications. For this, we consider the concurrence,intrinsic concurrence and first-order coherence, and evaluate the proposedtrade-off relations between them. In particular, we study the temporalevolution of a general two-qubit XYZ Heisenberg model with asymmetricspin-orbit interaction under decoherence and analyze the trade-off relations ofquantum resource theory. For XYZ Heisenberg model, we confirm that thetrade-off relation between intrinsic concurrence and first-order coherenceholds. Furthermore, we show that the lower bound of intrinsic concurrence isuniversally valid, but the upper bound is generally not. These relations inHeisenberg models can provide a way to explore how quantum resources aredistributed in spins, which may inspire future applications in quantuminformation processing.

Trade-off relations of quantum resource theory in Heisenberg models