Figure 1: MZI for single photons.
From: Equivalence of wave–particle duality to entropic uncertainty
Passing through the first beam splitter (BS) creates a superposition of which-path states, |0› and |1›, at time t1, then the system interacts with an environment E=E1E2. Finally, at time t2, a phase shift φ is applied to the lower arm and the two beams are recombined on a second beam splitter. (While this is the typical setup, our framework also allows E to play a more general role, for example, being correlated to the photon before it enters the MZI.) Our complementary guessing game proceeds as follows. In one game (coloured red), Alice tries to guess which of the two paths the photon took given that she has access to a portion of E denoted E1, which could be, for example, a gas of atoms whose internal states record information about the presence of a photon. In the other game (coloured blue), one of two phases, φ=φ0 or φ=φ0+π, is randomly applied to the lower interferometer arm and Alice tries to guess φ given that she has access to a different portion of E denoted E2, which could be, for example, the photon’s polarization. We argue that WPDRs impose fundamental trade-offs on Alice’s ability to win these two games.
