Quantitative wave-particle duality and nonerasing quantum erasure

Abstract

The notion of wave-particle duality may be quantified by the inequality V 2 + K 2 ≤ 1, relating interference fringe visibility V and path knowledge K. With a single-photon interferometer in which polarization is used to label the paths, we have investigated the relation for various situations, including pure, mixed, and partially-mixed input states. A quantum eraser scheme has been realized that recovers interference fringes even when no which-way information is available to erase. 03.65.Bz, 07.60.Ly Wave-particle duality (WPD) dates back to Einstein's seminal paper on the photoelectric effect [1], and is a striking manifestation of Bohr's complementarity principle [2] (for a formal definition see Ref.[3]). The familiar phrase "each experiment must be described either in terms of particles or in terms of waves" emphasizes the extreme cases and disregards intermediate situations, in which particle and wave aspects coexist. Theoretical investigations [4,5], supplemented by a few experimental studies [6,7], have led to a quantitative formulation of WPD [Eq. (1) below]. Here we report an experiment using a single-photon Mach-Zehnder interferometer in which polarization marks the path. We investigated the entire scope of the duality relation, for pure, mixed, and partially-mixed input states, and found absolute agreement at the percent level [8]. We also realized a novel quantum eraser scheme, whereby interference is recoverable although no which way (WW) information was available to erase. In view of the kinematical equivalence of all binary degrees of freedom, our results are directly applicable whenever an interfering particle is entangled with a 2-state quantum system.To quantify WPD, one needs quantitative, measurable characteristics for the wave-like and particle-like behavior of quanta. In an interferometer, the former is naturally quantified by the Visibility V of the observed interference fringes. The quantification of the latter is based on the Likelihood L of correctly guessing the path taken by a particular quantum -the better one can guess, the more pronounced are the particle aspects. A random guess gives L = 1 2 , whereas L = 1 indicates that the way is known with certainty. The actual WW Knowledge K is given by K = 2L − 1, with 0 ≤ K ≤ 1. In an asymmetric interferometer one way is more likely than the other to begin with (L a priori >

Duality of quantum coherence and path distinguishability

“…Thus, the knowledge of which-path information or the path distinguishability limits the interference visibility V in an interference experiment, according to the above complementarity relation. This relation has been demonstrated experimentally with atoms [6], nuclear magnetic resonance [7,8], faint lasers [9], and also with single photons [10]. Further, the complementarity relation has been extended to the more general case of an asymmetric interferometer where only a single output port is considered and this duality holds [11].…”

Interference of Quantum Channels

“…1) displays the key elements of quantum mechanics: the superposition of indistinguishable paths, and the complementarity of certain observables. Interference is a consequence of the possibility of the particle taking both paths, and any process which tends to label the path of the particle will reduce the magnitude of the interference [5].…”

Measuring a Photonic Qubit without Destroying It

“…The decline of K 2 + V 2 with increasing K can be attributed to the increasing requirement for non-classical (as well as classical) interference as the strength of the QND measurement is increased. In contradistinction to the non-destructive scheme presented here, previous tests of complementarity have relied on encoding which-path information onto a different degree of freedom of the interfering particles [25,26], so that which-path information is only obtained destructively, when the particles are measured.…”