Measuring Which-Path Information with Coupled Electronic Mach-Zehnder Interferometers
arXiv:1105.2587 · doi:10.1103/PhysRevB.85.045320
Abstract
We theoretically investigate a generalized "which-path" measurement on an electronic Mach-Zehnder Interferometer (MZI) implemented via Coulomb coupling to a second electronic MZI acting as a detector. The use of contextual values, or generalized eigenvalues, enables the precise construction of which-path operator averages that are valid for any measurement strength from the available drain currents. The form of the contextual values provides direct physical insight about the measurement being performed, providing information about the correlation strength between system and detector, the measurement inefficiency, and the proper background removal. We find that the detector interferometer must display maximal wave-like behavior to optimally measure the particle-like which-path information in the system interferometer, demonstrating wave-particle complementarity between the system and detector. We also find that the degree of quantum erasure that can be achieved by conditioning on a specific detector drain is directly related to the ambiguity of the measurement. Finally, conditioning the which-path averages on a particular system drain using the zero frequency cross-correlations produces conditioned averages that can become anomalously large due to quantum interference; the weak coupling limit of these conditioned averages can produce both weak values and detector-dependent semi-weak values.
17 pages, 12 figures, published version including appendix
References in corpus (27)
- Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification
- Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
- Weak values and the Leggett-Garg inequality in solid-state qubits
- Direct measurement of the coherence length of edge states in the Integer Quantum Hall Regime
- Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
- Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values
- Experimental Violation of Two-Party Leggett-Garg Inequalities with Semi-weak Measurements
- Dephasing in the electronic Mach-Zehnder interferometer at filling factor 2
- Finite bias visibility of the electronic Mach-Zehnder interferometer
- A double-slit `which-way' experiment on the complementarity--uncertainty debate
- Decoherence and single electron charging in an electronic Mach-Zehnder interferometer
- Conditional statistics of electron transport in interacting nanoscale conductors
- Edge Channel Interference Controlled by Landau Level Filling
- Resonant dephasing in the electronic Mach-Zehnder interferometer
- Decoherence and interactions in an electronic Mach-Zehnder interferometer
- Nonequilibrium Dephasing in an Electronic Mach-Zehnder Interferometer
- Pre- and post-selection, weak values, and contextuality
- The Behavior of Electronic Interferometers in the Non-Linear Regime
- Exactly Solved Model for an Electronic Mach-Zehnder Interferometer
- Tomography of many-body weak values: Mach-Zehnder interferometry
- Parity detection and entanglement with a Mach-Zehnder interferometer
- Electron interferometry in quantum Hall regime: Aharonov-Bohm effect of interacting electrons
- Multi-channel architecture for electronic quantum-Hall interferometry
- Dephasing by electron-electron interactions in a ballistic Mach-Zehnder interferometer
- Hardy's Test versus the CHSH Test of Quantum Non-Locality: Fundamental and Practical Aspects
- Violation of Bell's inequality in electronic Mach-Zehnder interferometers
- Electronic interferometer capacitively coupled to a quantum dot
Cited by in corpus (24)
- Colloquium: Understanding Quantum Weak Values: Basics and Applications
- The significance of the imaginary part of the weak value
- Weak Values are Interference Phenomena
- Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance
- Contextual-value approach to the generalized measurement of observables
- Demonstration of Weak Measurement Based on Atomic Spontaneous Emission
- An Electronic Quantum Eraser
- Quantum instruments as a foundation for both states and observables
- Sufficient conditions for uniqueness of the weak value
- Dynamical Scheme for Interferometric Measurements of Full-Counting Statistics
- Analytically solvable model of an electronic Mach-Zehnder interferometer
- Time-dependent simulation and analytical modelling of electronic Mach-Zehnder interferometry with edge-states wave packets
- Two-particle entanglement in capacitively coupled Mach-Zehnder interferometers
- Electron interference and entanglement in coupled 1D systems with noise
- Wave Function Collapse and the No-Superluminal-Signaling Principle
- Three Mach Zehnder Interferometers Setup for Production and Observation of GHZ-entanglement of Electrons
- Probing Quantitatively Two-electron Entanglement with a Spintronic Quantum Eraser
- Detection of quantum interference without interference
- Quantum computing through electron propagation in the edge states of quantum spin Hall systems
- Effective electrostatic attraction between electrons due to quantum interference
- How to extract weak values from a mesoscopic electronic system
- Erasing the which-path information of photons
- Monitored quantum transport: full counting statistics of a quantum Hall interferometer
- Ballistic 3-port interferometric logic gates in the quantum Hall regime