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 $f^{†}|\Omega ⟩$.

arXiv comment14 pages, 3 figures; minor changes (3 new citations, a remark on fermionic systems)

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Cited by in corpus (14)

• Entanglement by Path Identity
• Interference of Identical Particles from Entanglement to Boson-Sampling
• Random bosonic states for robust quantum metrology
• Quantum Experiments and Graphs II: Quantum Interference, Computation and State Generation
• Quantum-limited Euler angle measurements using anticoherent states
• Hard limits on the postselectability of optical graph states
• Perfect polarization for arbitrary light beams
• Multipartite quantum correlations: symplectic and algebraic geometry approach
• No-go theorems for photon state transformations in quantum linear optics
• Arbitrary entanglement of three qubits via linear optics
• Visualizing quantum mechanics in an interactive simulation -- Virtual Lab by Quantum Flytrap
• Applications of differential geometry and representation theory to description of quantum correlations
• Multiphoton, multimode state classification for nonlinear optical circuits
• Rigorous no-go theorems for heralded linear-optical state generation tasks