2019/01/23 by Filippus S. Roux, Roux, Filippus S., Nicolas Fabre +1 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Optics (physics.optics) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.1901.07782
openalex publication_date 2019/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the quadrature bases that incorporate the spatiotemporal degrees of freedom, we develop a Wigner functional theory for quantum optics, as an extension of the Moyal formalism. Since the spatiotemporal quadrature bases span the complete Hilbert space of all quantum optical states, it does not require factorization as a tensor product of discrete Hilbert spaces. The Wigner functions associated with such a space become functionals and operations are expressed by functional integrals -- the functional version of the star product. The resulting formalism enables tractable calculations for scenarios where both spatiotemporal degrees of freedom and particle-number degrees of freedom are relevant. To demonstrate the approach, we compute examples of Wigner functionals for a few well-known states and operators.