Duality relations in a two-path interferometer with an asymmetric beam splitter

Abstract

We investigate quantitatively the wave-particle duality in a general Mach-Zehnder interferometer setup with an asymmetric beam splitter. The asymmetric beam splitter introduces additional a priori which-path knowledge, which is different for a particle detected at one output port of the interferometer and a particle detected at the other. Accordingly, the fringe visibilities of the interference patterns emerging at the two output ports are also different. Hence, in sharp contrast with the symmetric case, here we should concentrate on one output port and distinguish two possible paths taken by the particles detected at that port among four paths. It turns out that two nonorthogonal unsharp observables are measured jointly in this setup. We apply the condition for joint measurability of these unsharp observables to obtain a trade-off relation between the fringe visibility of the interference pattern and the which-path distinguishability.

Equivalence of wave–particle duality to entropic uncertainty

“…To prove equation (10), we need to restrict the form of C 0 . We show that equation (10) holds so long as C 0 is unbiased with respect to the whichpath basis Z on the subspace Q. Fortunately, this condition is satisfied for all three types of interferometers in Figs 1, 2 and 3. More precisely, it is satisfied for the MZI provided BS 2 is 50/50, for the Franson case provided both BS 2 (the second beam splitters in Fig.…”

“…First, it is obvious from the operational meaning of the conditional min-entropy in the first of equations (6) 2 , and second we use our result equation (10) to rewrite equation (11) as equation (1). As emphasized in ref.…”

“…To show this, we must prove equation (10), which relates our entropic measure of wave behaviour in the second of equations (4) to fringe visibility, and we now do this for generic binary interferometers. We remark that one can take equation (7) as a generic definition for fringe visibility, where the label D 0 is arbitrary, that is, it corresponds to some arbitrary detector.…”

“…In reality, it contains the only mystery [of quantum mechanics]. ' Many quantitative statements of this idea, so-called WPD relations (WPDRs), have been formulated [2][3][4][5][6][7][8][9][10][11][12][13] . Such relations typically consider the Mach-Zehnder interferometer (MZI) for single photons, see Fig.…”

Chaotic Fractal Tiling for the Missing Dark Energy and Veneziano Model

“…In addition we discuss some recent advances in our understanding of basic problems connected to fundamental questions in quantum mechanics and cosmology [33][34][35][36][37][38][39][40][41].…”