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...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.023125 |
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| 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 |
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