Paradoxical behavior in a triple cascade of Mach–Zehnder interferometers

Abstract

A gedanken experiment is considered using a cascade of three Mach-Zehnder interferometers (MZIs). The first MZI in the cascade is used to judiciously prepare the pre-selected state of a single photon launched into one of its input ports and the third MZI in the cascade is used to judiciously prepare the postselected state of the photon emerging from one of its output ports. Paradoxical behavior arises when a weak measurement of photon occupation number is independently performed along each of the two paths emerging from the first MZI's output ports, i.e., the pointer associated with the weak measurement along one path registers a large positive occupation number and that for the weak measurement along the other path registers a large negative occupation number. Although each of these measurements contradicts the fact that there is only one photon in the interferometer, quantum mechanics resolves this paradox in an interesting way by ensuring that the sum of these occupation numbers is always 1.

A weak-value model for virtual particles supplying the electric current in graphene: the minimal conductivity and the Schwinger mechanism

“…We have obtained the linearity of the electric current, namely, the quasi-Ohmic. The estimated conductivity (39) almost accords with the minimal conductivity ∼ e 2 /h per channel, especially the theoretical value like e 2 /(πh). In this case, δE bal /2E-fold virtual particles play roles of the electric carriers per state.…”

“…In solid systems, such an effect has been used for charge sensing [33] and atomic spontaneous emission [34]. In addition to the applications mentioned above, weak measurements have offered interesting approaches for the foundation of quantum mechanics such as quantum paradoxes [35][36][37][38][39] and the violation of the Leggett-Garg inequality [40][41][42][43]. Apart from weak measurements, a weak value has been useful for explaining quantum phenomena [17,18,[44][45][46][47].…”

Exact pointer theories for von Neumann projector measurements of pre- and postselected and preselected-only quantum systems: statistical mixtures and weak value persistence

“…These operators are also interesting because the measurement and interpretation of their weak values have played a central role in the theoretical and experimental resolutions of the 'quantum box problem' [16][17][18] and 'Hardy's paradox' [19][20][21][22][23]. More recently, projector weak values have also been used to investigate paradoxical behaviour in Mach-Zehnder interferometers (MZIs) [24] and employed in experimental observations of dynamical quantum non-locality-induced effects [25][26][27].…”