2016/12/17 by L. Rosales-Zárate, Rosales-Zárate, L., R. Y. Teh +7
Health Professions · Physics and Astronomy · Social Sciences · #Adolescent Sexual and Reproductive Health #FOS: Physical sciences #Family Dynamics and Relationships #Marriage and Sexual Relationships #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1612.05727
12 pages plus 4 pages Appendices, 12 Figures
arxiv created 2016/12/17 · openalex publication_date 2016/12/17 · arxiv updated 2016/12/20 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
We consider three modes A, B and C and derive continuous variable monogamy inequalities that constrain the distribution of bipartite entanglement amongst the three modes. The inequalities hold for all such tripartite states, without the assumption of Gaussian states, and are based on measurements of two conjugate quadrature phase amplitudes Xi and Pi at each mode i=A,B. The first monogamy inequality is DBA+DBC≥1 where DBA<1 is the widely used symmetric entanglement criterion, for which DBA is the sum of the variances of (XA-XB)/2 and (PA+PB)/2. A second monogamy inequality is EntBAEntBC≥\frac1(1+(gBA(sym))2)(1+(gBC(sym))2) where EntBA<1 is the EPR variance product criterion for entanglement. Here EntBA is a normalised product of variances of XB-gBA(sym)XA and PB+gBA(sym)PA, and gBA(sym) is a parameter that gives a measure of the symmetry between the moments of A and B. We also show that the monogamy bounds are increased if a standard steering criterion for the steering of B is not satisfied. We illustrate the monogamy for continuous variable tripartite entangled states including the effects of losses and noise, and identify regimes of saturation of the inequalities. The monogamy relations explain the experimentally observed saturation at DAB=0.5 for the entanglement between A and B when both modes have 50% losses, and may be useful to establish rigorous bounds of correlation for the purpose of quantum key distribution protocols.