Bipartite entangled Gaussian states provide an important resource for quantum information based on continuous variables. Perfect complementarity between one-particle visibility and two-particle visibility in discrete systems, has been previously generalized to an inequality, rather than equality, for Gaussian states characterized by varying amounts of squeezing and entanglement. The latter quantum inequality, however, appears to be due to assessment of two-particle visibility using an indirect method that first corrects the two-particle probability distribution by adding and subtracting distributions with varying degree of entanglement. In this work, we develop a new direct method for quantifying two-particle visibility based on measurement of a pair of two-particle observables that commute with the measured pair of single-particle observables. This direct method treats the two pairs of quantum observables on equal footing by formally identifying all four observable distributions as Radon transforms of the original two-particle probability distribution. The quantum complementarity relation between one-particle visibility and two-particle visibility obtained through the direct method deviates from unity by an exponentially small quantity bounded by the amount of squeezing, which is shown to vanish in the limit of infinite squeezing when the entangled Gaussian state approaches an ideal Einstein-Podolsky-Rosen state. The presented results demonstrate the theoretical utility of Radon transforms for elucidating the nature of two-particle visibility and provide new tools for the development of quantum applications employing continuous variables.
|Original language||English GB|
|Issue number||arXiv:2012.12338 [quant-ph]|
|State||Published - 2020|
- Quantum Physics