Average Rényi entanglement entropy in Gaussian boson sampling

Journal Article · 07 May 2025 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.7.023125 · OSTI ID:2565016

Youm, Jason ; Iosue, Joseph T. ; Ehrenberg, Adam ; Wang, Yu-Xin ; Gorshkov, Alexey V.

Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian boson sampling, where quadratic photonic input states are interfered via a linear optical unitary and subsequently measured in the Fock basis. In this paper, we study the modal entanglement of the output states in this framework just before the measurement stage. Specifically, we compute Page curves as measured by various Rényi- $\alpha$ entropies, where the Page curve describes the entanglement between two partitioned groups of output modes averaged over all linear optical unitaries. We derive these formulas for $\alpha =1$ (i.e., the von Neumann entropy) and, more generally, for all positive integer $\alpha$ , in the asymptotic limit of infinite number of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength. We then analyze the limiting behaviors when the squeezing is small and large. Having determined the averages, we then explicitly calculate the Rényi- $\alpha$ variance for integers $\alpha >1$ and are able to show that these entropies are weakly typical. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0019040; SC0024220
• OSTI ID: 2565016
• Journal Information: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 2 Vol. 7; ISSN 2643-1564; ISSN PPRHAI
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English