Embezzlement of entanglement is the counterintuitive process in which entanglement is extracted from a resource system using local unitary operations, with almost no detectable change in the resource's state. It was recently argued that any state of a relativistic quantum field theory can serve as a resource for perfect embezzlement. We study the circuit complexity of embezzlement using sequences of states that enable arbitrary precision for the process, commonly called universal embezzling families. In addition, we argue that this approach provides a well-defined model for the complexity of embezzlement from quantum field theories. Under fairly general assumptions, we establish a generic lower bound on the complexity, which increases with the precision of the process or the amount of embezzled entanglement, and diverges as either becomes infinite. As an example, we consider a one-dimensional critical system as the resource and derive an exponentially growing lower bound on the complexity. Consequently, the findings imply that circuit complexity acts as a physical obstruction to perfect embezzlement. Supplementary to the main results, we derive lower bounds for common models of circuit complexity for state preparation based on the difference between the Schatten norms of the initial and final states.

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• Computational complexity
• Quantum control
• Quantum entanglement
• Quantum field theory
• Quantum information theory