Complementarity of fringe visibilities in three-particle quantum mechanics (Q2739497)

From the test: In an \(n\)-particle quantum system there are, in general, distinct and independent types of interference fringes. While ignoring all except one of the particles, one may subject the chosen particle to some adjustable apparatus and thereby cause the count rate at a detector to oscillate, i.e. single-particle fringes. While totally ignoring all but two of the particles, one may make apparatus adjustments that cause oscillations in the coincident count rate at two detectors, i.e. two-particle fringes. Similarly, if the system contains enough particles, one may cause oscillations in the coincident count rates at three, four, or more detectors, thereby creating three-particle and four-particle fringes, etc. In general, since a portion of the \(n\)-particle fringing may be simply due to products of lower order fringes, the ``raw'' \(n\)-particle fringes may not be independent of these lower order fringes. However, after subtracting off all contamination due to lower order products, some \(n\)-particle oscillations may remain. These are the ``true'' \(n\)-particle fringes and they are always associated with the presence of entanglement at the \(n\)-particle level. For two-particle systems there is a striking complementarity in the visibility, \(\nu_1\), of the single-particle fringes and the visibility, \(\nu_{12}\), of the true two-particle fringes: \(v^2_1+ v^2_{12}\leq 1\). Does complementarity extend to three particles simply as \(v^2_1+ v^2_{12}+ v^2_{123}\leq 1\), where \(\nu_{123}\) is the visibility of the true three-particle fringes?NEWLINENEWLINEFor the entire collection see [Zbl 0959.00017].