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FRI: Friday Contributed Sessions

FRI 7: Entanglement and Complexity: Contributed Session to Symposium III

FRI 7.1: Vortrag

Freitag, 12. September 2025, 10:45–11:00, ZHG008

Entanglement theory with limited computational resources — Lorenzo Leone, Jacopo Rizzo, Jens Eisert, and •Sofiene Jerbi — Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Germany

The precise quantification of the ultimate efficiency in manipulating quantum resources lies at the core of quantum information theory. However, purely information-theoretic measures fail to capture the actual computational complexity involved in performing certain tasks. In this work, we rigorously address this issue within the realm of entanglement theory. We consider two key figures of merit: the computational distillable entanglement and the computational entanglement cost, quantifying the optimal rate of entangled bits (ebits) that can be extracted from or used to dilute many identical copies of n-qubit bipartite pure states, using computationally efficient LOCC. We demonstrate that computational entanglement measures diverge significantly from their information-theoretic counterparts. While the von Neumann entropy captures information-theoretic rates for pure-state transformations, we show that under computational constraints, the min-entropy instead governs optimal entanglement distillation. Meanwhile, efficient entanglement dilution requires maximal (Ω(n)) ebits even for nearly unentangled states. Our results establish a stark, maximal separation of Ω(n) vs o(1) between computational and information-theoretic entanglement measures. Finally, we find new sample-complexity bounds for measuring and testing the von Neumann entropy, efficient state compression, and efficient LOCC tomography protocols.

Keywords: entanglement theory; quantum information; computational complexity