Average Rényi entanglement entropy in Gaussian boson sampling

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 mea...

Full description

Saved in:
Bibliographic Details
Main Authors: Jason Youm, Joseph T. Iosue, Adam Ehrenberg, Yu-Xin Wang, Alexey V. Gorshkov
Format: Article
Language:English
Published: American Physical Society 2025-05-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.7.023125
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849324067901931520
author Jason Youm
Joseph T. Iosue
Adam Ehrenberg
Yu-Xin Wang
Alexey V. Gorshkov
author_facet Jason Youm
Joseph T. Iosue
Adam Ehrenberg
Yu-Xin Wang
Alexey V. Gorshkov
author_sort Jason Youm
collection DOAJ
description 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.
format Article
id doaj-art-672de00ee69a4ad6a93977c8cf93628f
institution Kabale University
issn 2643-1564
language English
publishDate 2025-05-01
publisher American Physical Society
record_format Article
series Physical Review Research
spelling doaj-art-672de00ee69a4ad6a93977c8cf93628f2025-08-20T03:48:51ZengAmerican Physical SocietyPhysical Review Research2643-15642025-05-017202312510.1103/PhysRevResearch.7.023125Average Rényi entanglement entropy in Gaussian boson samplingJason YoumJoseph T. IosueAdam EhrenbergYu-Xin WangAlexey V. GorshkovRecently, 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.http://doi.org/10.1103/PhysRevResearch.7.023125
spellingShingle Jason Youm
Joseph T. Iosue
Adam Ehrenberg
Yu-Xin Wang
Alexey V. Gorshkov
Average Rényi entanglement entropy in Gaussian boson sampling
Physical Review Research
title Average Rényi entanglement entropy in Gaussian boson sampling
title_full Average Rényi entanglement entropy in Gaussian boson sampling
title_fullStr Average Rényi entanglement entropy in Gaussian boson sampling
title_full_unstemmed Average Rényi entanglement entropy in Gaussian boson sampling
title_short Average Rényi entanglement entropy in Gaussian boson sampling
title_sort average renyi entanglement entropy in gaussian boson sampling
url http://doi.org/10.1103/PhysRevResearch.7.023125
work_keys_str_mv AT jasonyoum averagerenyientanglemententropyingaussianbosonsampling
AT josephtiosue averagerenyientanglemententropyingaussianbosonsampling
AT adamehrenberg averagerenyientanglemententropyingaussianbosonsampling
AT yuxinwang averagerenyientanglemententropyingaussianbosonsampling
AT alexeyvgorshkov averagerenyientanglemententropyingaussianbosonsampling