Elitzur–Vaidman Bomb Tester (2D)

Bomb Type

Ready — press Fire.

Computed Probabilities

P(explode)

—

P(interaction-free)

—

P(bright port, no info)

—

|amp arm B|² at BS1

—

Trial Statistics

Exploded

IFM success

No info

Trials run

Empirical IFM rate

—

How it works

A single photon enters a Mach-Zehnder interferometer: two 50/50 beam splitters (BS1, BS2) joined by a safe arm A (top) and a test arm B (bottom) that may hold a bomb. Every beam splitter here is the real unitary matrix

[out1]   1  [1  i] [in1]
[out2] = -- [    ] [    ]
         √2 [i  1] [in2]

applied to complex amplitudes with actual re/im components — the same function computes both splitters, so nothing about the outcome probabilities is hand-typed.

No bomb / dud bomb — the two arms recombine at BS2 with perfect destructive interference into the dark port and constructive interference into the bright port: 100% bright, 0% dark, exactly as unperturbed quantum interference predicts.
Live bomb — placing an absorber in arm B is a which-path measurement. With probability |amp_B|² = 1/2 the bomb absorbs the photon and explodes. With probability 1/2 the photon is found (collapsed) in arm A alone — the superposition that made the dark port destructively silent is now gone, so BS2 splits this lone amplitude 50/50: a dark-port click (25% of all trials) proves a live bomb sits in the arm without a single photon ever touching it; a bright-port click (25%) is inconclusive.

Net analytic result: P(explode) = 1/2, P(interaction-free detection) = 1/4, P(no information) = 1/4 — the original 1993 Elitzur–Vaidman scheme. Every number on this page is the |amplitude|² of a complex state actually computed by the beam-splitter function above, and the trial counters converge to these fractions purely from repeated random sampling of those computed probabilities.

Photon amplitude Dark port (interaction-free) Bright port (no info) Live bomb / explosion

Elitzur–Vaidman Bomb Tester (2D) — Real Complex-Amplitude Interferometer