Oneparticle and twoparticle visibilities in bipartite entangled Gaussian states
Abstract
Complementarity between oneparticle visibility and twoparticle visibility in discrete systems can be extended to bipartite quantumentangled Gaussian states implemented with continuousvariable quantum optics. The meaning of the twoparticle visibility originally defined by Jaeger, Horne, Shimony, and Vaidman with the use of an indirect method that first corrects the twoparticle probability distribution by adding and subtracting other distributions with varying degree of entanglement, however, deserves further analysis. Furthermore, the origin of complementarity between oneparticle visibility and twoparticle visibility is somewhat elusive and it is not entirely clear what is the best way to associate particular twoparticle quantum observables with the twoparticle visibility. Here, we develop a direct method for quantifying the twoparticle visibility based on measurement of a pair of twoparticle observables that are compatible with the measured pair of singleparticle observables. For each of the twoparticle observables from the pair is computed corresponding visibility, after which the absolute difference of the latter pair of visibilities is considered as a redefinition of the twoparticle visibility. Our approach reveals an underlying mathematical symmetry as it treats the two pairs of oneparticle or twoparticle observables on equal footing by formally identifying all four observable distributions as rotated marginal distributions of the original twoparticle probability distribution. The complementarity relation between oneparticle visibility and twoparticle visibility obtained with the direct method is exact in the limit of infinite Gaussian precision where the entangled Gaussian state approaches an ideal EinsteinPodolskyRosen state. The presented results demonstrate the theoretical utility of rotated marginal distributions for elucidating the nature of twoparticle visibility and provide tools for the development of quantum applications employing continuous variables.
 Publication:

Physical Review A
 Pub Date:
 June 2021
 DOI:
 10.1103/PhysRevA.103.062211
 arXiv:
 arXiv:2012.12338
 Bibcode:
 2021PhRvA.103f2211G
 Keywords:

 Quantum Physics
 EPrint:
 Revised version, 18 pages, 7 figures, accepted to PRA