Work

Average Rényi entanglement entropy in Gaussian boson sampling

Year: 2025

Type: article

Abstract: 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- α 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 α = 1 (i.e., the von Neumann entropy) and, more generally, for all positive integer α , 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- α variance for integers α > 1 and are able to show that these entropies are weakly typical.

Source: Physical Review Research

DOI: 10.1103/physrevresearch.7.023125

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

Institutions: Joint Center for Quantum Information and Computer Science, Joint Quantum Institute, University of Maryland, College Park

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625