Information gain versus interference in Bohr’s principle of complementarity

Abstract

Based on modern quantum measurement theory, we use Zurek's "triple model" to study, from the viewpoint of quantum information theory, the wave and particle nature of a photon in a symmetric Mach-Zehnder interferometer. In the process of quantum measurement, the state of both the system and the detector is not an entangled state but a correlated state. We find that the information gain about the photon is related to the correlations (including classical and quantum correlations) between the photon and the detector. We also derive the relationship between the information gain and the fringe visibility. We find that the classical correlations remain consistent with the path distinguishability and can be used to describe the particle-like property of the photon. Quantum correlations are not exactly the same as fringe visibility, but both can represent the quantum coherence of the photon. Finally, we provide an analytical expression for quantum correlations of one type of two-qubit separable states.

Fringe visibility and correlation in Mach-Zehnder interferometer with an asymmetric beam splitter

“…Liu et al [39] have demonstrated that D(ρ QD 2 ) and V do not satisfy the complementarity when S x = − cos β = 0 and the input particle is in pure state. For the more general case we discuss in this section, when the final state of the particle and the WPD is in mixed state, the…”

Coherent Polarization States Multiplexer and Its Feasibility in Quantum Communication

“…Most of the CV-QKD were conducted while splitting signal and LO as Mach-Zehnder interferometer's two arms [15][16][17]. Atmospheric scattering adds difficulty to synchronization in free space for the two beams, and it's also hard for an accurate interference of them at Bob's side.…”

“…Continuous-variable QKD (CV-QKD), as one of the implementation schemes of QKD, possesses several advantages over DV-QKD: easier implementation [9][10][11] and lower cost [12][13][14], etc. Most of the CV-QKD systems were performed while splitting signal and LO as Mach-Zehnder interferometer's two arms [15][16][17]. Atmospheric scattering adds difficulty to synchronization of the two beams in free space, and it's also hard for an accurate interference of them at Bob's side.…”

Proposal to test quantum wave-particle superposition on massive mechanical resonators

“…The arrangement rules out a hidden-variable theory, which suggests that the photon may determine, in advance, which behavior, wave or particle, to exhibit through a hidden variable. [4][5][6][7][8][9][10][11] Recently, a quantum delayed-choice experiment, where BS 2 is engineered to be in a quantum superposition of being present and absent, has been proposed. 12 Such a version allows a single system to be in a quantum superposition of a wave and a particle, so that both behaviors can be observed in a single measurement apparatus at the same time.…”