2 IntroductionComplementarity, the incomplete nature of a quantum measurement -a core concept in quantum mechanics -stems from the choice of the measurement apparatus 1 . The notion of complementarity is closely related to Heisenberg's uncertainty principle, but the exact relation between the two remains a source of debate [2][3][4][5][6][7][8] . For example, knowledge of a particle's position in a double slit interference experiment will quench its wave-like nature and, vice versa, observing the wave property via interference implies lack of knowledge of the particle's path. A canonical system for exploring complementarity is the quantum eraser (QE), predominantly studied thus far in photonic systems [9][10][11][12][13][14] . A QE is an interference experiment consisting of two stages. First, one of the interfering paths is coupled to a 'which path' (WP) detectordemonstrating loss of interference due to acquisition of WP information. Second, the WP information is being 'erased' by projecting the detector's wavefunction on a particular basis; this renders the WP information inaccessible, thus allowing reconstruction of the interference pattern.In this work, we present a first implementation of a QE in an electronic system. Our system consists of two identical electronic Mach-Zehnder interferometers (MZIs) 15 entangled via Coulomb interactions. Such novel setup has already attracted a considerable theoretical attention [16][17][18] . With one MZI serving as a path detector and the other as the system interferometer, the visibility of the Aharonov-Bohm oscillation in the System can be controlled by the Detector. We demonstrate how a continuous change of the measurement basis, followed by post selection (via cross correlation of current fluctuations), allows a smooth transition between keeping and erasing the WP information. Theory Mach-Zehnder interferometerAn electronic MZI is formed by manipulating quasi one dimensional, chiral edge channels, which are formed in the integer quantum Hall effect regime 15 . Such a realization allows directing the path of electrons at will -leading to high visibility interference pattern. Potential barriers, formed by quantum point contacts (QPCs), take the role of optical beam splitters, transmitting and reflecting impinging electrons with amplitudes i t and i r , respectively, with 1 2 2Two such coupled MZIs are shown in Fig. 1, where the coupling is mediated by the lower path of the System and the upper path of the Detector, referred to as interacting paths (shaded area in Fig. 1a). Starting with the System, an electron injected from Source S1 arrives at SQPC1 and is put into a superposition of being reflected into the interacting path and transmitted into the noninteracting path, namely: Here, e h = Φ 0 is the magnetic flux quantum, A the area enclosed by the two paths, and B the magnetic field. The visibility of the interfering pattern at D2 is defined asThroughout our experiments, all the QPCs were tuned to have equal transmission and reflection amplitudes, Entangling tw...

Controlled dephasing of electrons, via 'which path' detection, involves, in general, coupling a coherent system to a current driven noise source. However, here, we present a case in which a nearly isolated electron puddle at thermal equilibrium strongly affects the coherence of a nearby electronic interferometer. Moreover, for certain average electron occupations of the puddle, the interferometer exhibits complete dephasing. This robust phenomenon stems from the Friedel Sum Rule, which relates a system's occupation with its scattering phases. The interferometer opens a peeping window into physics of the isolated electron puddle, which cannot be accessed otherwise.