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arXiv · 1403.3069

Which multiphoton states are related via linear optics?

Piotr Migdał·Javier Rodríguez-Laguna·Michał Oszmaniec·Maciej Lewenstein
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Abstract

We investigate which pure states of $n$ photons in $d$ modes can be transformed into each other via linear optics, without post-selection. In other words, we study the local unitary (LU) equivalence classes of symmetric many-qudit states. Writing our state as $f^\dagger|Ω\rangle$, with $f^\dagger$ a homogeneous polynomial in the mode creation operators, we propose two sets of LU-invariants: (a) spectral invariants, which are the eigenvalues of the operator $ff^\dagger$, and (b) moments, each given by the norm of the symmetric component of a tensor power of the initial state, which can be computed as vacuum expectation values of $f^k(f^\dagger)^k$. We provide scheme for experimental measurement of the later, as related to the post-selection probability of creating state $f^{\dagger k}|Ω\rangle$ from $k$ copies of $f^{\dagger}|Ω\rangle$.

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Piotr Migdał, Javier Rodríguez-Laguna, Michał Oszmaniec, Maciej Lewenstein. 2014-04-14. Which multiphoton states are related via linear optics?. https://doi.org/10.1103/physreva.89.062329

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