Which multiphoton states are related via linear optics?

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 $f^{†}|\Omega ⟩$, with $f^{†}$ 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 $f{f}^{†}$, 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 $f^k(f^{†}{)}^k$. We provide scheme for experimental measurement of the later, as related to the post-selection probability of creating state $f^{†k}|\Omega ⟩$ from $k$ copies of $f^{†}|\Omega ⟩$.

14 pages, 3 figures; minor changes (3 new citations, a remark on fermionic systems)

References in corpus (4)

• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Many-particle interference beyond many-boson and many-fermion statistics
• Protecting an optical qubit against photon loss
• Symmetric entanglement classes for n qubits

Cited by in corpus (2)

• Entanglement by Path Identity
• Applications of differential geometry and representation theory to description of quantum correlations