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arXiv · 2404.00126

Pseudoentanglement Ain't Cheap

Sabee Grewal·Vishnu Iyer·William Kretschmer·Daniel Liang
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Abstract

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.

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Sabee Grewal, Vishnu Iyer, William Kretschmer, Daniel Liang. 2024-03-29. Pseudoentanglement Ain't Cheap. https://doi.org/10.1103/v493-8s1q

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