Pseudoentanglement Ain't Cheap
<|reference_start|>Pseudoentanglement Ain't Cheap: We show that any pseudoentangled state ensemble with a gap of $t$ bits of entropy requires $\Omega(t)$ non-Clifford gates to prepare. This bound is tight up to polylogarithmic factors if linear-time quantum-secure pseudorandom functions exist. Our result follows from a polynomial-time algorithm to estimate the entanglement entropy of a quantum state across any cut of qubits. When run on an $n$-qubit state that is stabilized by at least $2^{n-t}$ Pauli operators, our algorithm produces an estimate that is within an additive factor of $\frac{t}{2}$ bits of the true entanglement entropy.<|reference_end|>
@article{grewal2024pseudoentanglement,
    title={Pseudoentanglement Ain't Cheap},
    author={Sabee Grewal and Vishnu Iyer and William Kretschmer and Daniel Liang},
    journal={arXiv preprint arXiv:2404.00126},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.00126},
    primaryClass={quant-ph cs.CC}
}