Since interference is possible with a single photon, both interfering signals of a photon, after passing a beam-splitter, arrive at the detector with a phase-shift. No upper limit of this phase-shift is known. Therefore a test setup as shown in Fig.1 should answer the question, which way the photon took.
The laser radiation is down-converted by a BBO crystal to the two entangled beams “SIGNAL” and “IDLER” which are separated by a Glan-Thompson-Prism. The “IDLER” beam is received by detector “D1” which feeds it's signal to the “Start” input of the time-to-phase converter “TPC”.
The “Signal” beam is splitted by the 50% : 50% beam-splitter “BS” into “PATH1” and “Path2” after passing the mirrors “M1” and “M2”.
In “Path1” there is the variable phase-shifter “PS1” which allows a phase shift in this path by 0 <= ps1 < 2Pi.
In “Path2” there is the phase-shifter “PS2” with ps2 = n*2Pi with n>>1.
After passing the phase-shifters both signals converge on the lens “L” and interfere in it's focus on detector “D2” which feeds its signal to the “Stop” input of the “TPC”.
The level of interference and thereby the count-rate at “D1” can be determined by “PS1”.
“PS2” doesn't influence the interference at “D1” but introduces a time-delay in “Path2”.
Which path is triggering the detection of the interference-signal at “D1” can be seen at the output “PD” of the “TPC”.
If pd = ps1 it is “PATH1”.
If pd = ps2 it is “PATH2”.
If that's not true, the notion of a photon passing by “PATH1” or “PATH2” is wrong.
Or am I wrong ?
FIG1 : Test setup for which-way-information