## Entanglement in the full state vector of boson sampling

Yulong Qiao, Joonsuk Huh, Frank Grossmann

SciPost Phys. 15, 007 (2023) · published 12 July 2023

- doi: 10.21468/SciPostPhys.15.1.007
- Submissions/Reports

### Abstract

The full state vector of boson sampling is generated by passing $S$ single photons through beam splitters of $M$ modes. We express the initial Fock state in terms of 2$^{S-1}$ generalized coherent states, making possible the exact application of the unitary evolution. Due to the favorable polynomial scaling of numerical effort in $M$, we can investigate Rényi entanglement entropies for moderate particle and huge mode numbers. We find symmetric Page curves with a maximum entropy at equal partition, which is almost independent on Rényi index. Furthermore, the maximum entropy as a function of mode index saturates for $M\geq S^2$ in the collision-free subspace case. The asymptotic value of the entropy increases linearly with $S$. In addition, we show that the build-up of the entanglement leads to a cusp in the asymmetric entanglement curve. Maximum entanglement is reached well before the mode population is distributed over the whole system.

### Cited by 1

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}^{2}Yulong Qiao, -
^{3}Joonsuk Huh, -
^{2}Frank Grossmann

^{1}Max-Planck-Institut für Physik komplexer Systeme / Max Planck Institute for the Physics of Complex Systems^{2}Technische Universität Dresden / Dresden University of Technology [TUD]^{3}성균관대학교 / Sungkyunkwan University [SKKU]