  In interferometers, the more information about the quanta's path available in
an ancillary quantum system (AQS), the less visibility the interference has. By
use of Shannon entropy, we try to compare the amount of which-phase information
with the amount of which-way information stored in the AQS of two-path
interferometers with symmetric beam merging. We show that the former is lower
than or equal the latter if the bipartite system of the single-quanta and the
AQS is initially prepared in a pure state and the interaction between the two
parts is unitary. Especially when there exists symmetry, the equality holds. No
which-way information is obtained by the measurement that we use for extracting
the which-phase information and vice versa. In order to verify the results
experimentally, we propose assembling a new single-photon interferometer.
