Two Interferometric Complementarities

Gregg Jaeger

Department of Physics, Boston University, Boston, MA 02215.

Abner Shimony

Departments of Physics and Philosophy, Boston University, Boston, MA 02215.

Lev Vaidman

Department of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.

July 22, 1994

Abstract:

Two interferometric complementarities are formulated and demonstrated, and relations between them are analyzed. The first relates the distinguishability D(P) of the path of propagation of a particle (where P is the preparation of an ensemble) to the fringe visibility v_1 when amplitudes from two paths are combined. It is shown that [maxD(P)]^2+v_1^2=1, where the maximum is taken over all preparations compatible with a fixed density operator. The second complementarity relates the visibility of one-particle interference fringes to the visibility v_{12} of two-particle fringes: (v_{12})^2+(v_{1})^2 (< or =) 1. With a suitable extension of operations on the pair of particles, this inequality is strengthened to an equality.

PACS number(s): 03.65.Bz, 07.60.Ly