Wave-particle duality of unpolarized photons

Abstract

Photons in a two-path interferometer best embody wave-particle duality (WPD), which is a core concept of quantum theory. So far, the WPD relation is commonly written as $V^2+D^2\le 1$, where $V$ is the interference fringe visibility and $D$ is path distinguishability, i.e., the distinguishability of which path a photon passed. This inequality is saturated only when the which-way marker (WWM), which embodies which-path information (WPI) via an internal degree of freedom of photons, such as polarization, is in a pure state. For mixed-state WWM, conventionally defined distinguishability underestimates the amount of WPI and thus does not saturate the WPD relation. Here, we introduce a generalized measure of distinguishability $D$ that properly quantifies the WPI and saturates the WPD relation for all pure- and mixed-state WWM within a purification-based framework. To this end, mixed-state WWM is treated as a result of entanglement formation between the WWM and an external degree of freedom, e.g., environment, and $D$ is defined so that it incorporates the total WPI shared between the WWM and the environment. We show that $D$ thus defined is experimentally quantifiable, independently of $V$, without access to the environment. We experimentally evaluate $V$ and $D$ using true single photons generated in the completely mixed (unpolarized) state, and thus verify the saturated WPD relation.

arXiv comment17 pages, 4 figures

References in corpus (26)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement of a Pair of Quantum Bits
• Universal state inversion and concurrence in arbitrary dimensions
• Experimental realization of Wheeler's delayed-choice GedankenExperiment
• A Delayed Choice Quantum Eraser
• A double-slit quantum eraser
• Delayed-choice gedanken experiments and their realizations
• Entanglement-enabled delayed choice experiment
• Controlled double-slit electron diffraction
• Quantitative wave-particle duality and non-erasing quantum erasure
• Delayed-choice test of complementarity with single photons
• Bohr's Complementarity: Completed with Entanglement
• Measurement of geometric phase for mixed states using single photon interferometry
• Single photon wavefront-splitting interference: An illustration of the light quantum in action
• Coherence Constraints and the Last Hidden Optical Coherence
• Illustration of quantum complementarity using single photons interfering on a grating
• Polarization Coherence Theorem
• Turning off quantum duality
• Predictability, Distinguishability and Entanglement
• On the connection between Complementarity and Uncertainty Principles in the Mach-Zehnder interferometric setting
• Experimental observation of polarization coherence theorem
• Observing momentum disturbance in double-slit "which-way" measurements
• Afshar's Experiment does not show a Violation of Complementarity
• Coherence properties of a single dipole emitter in diamond
• Quantification and observation of genuine three-party coherence: A solution based on classical optics
• Multipath Wave-Particle Duality in Classical Optics