Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox

Abstract

It has been proposed that the ability to perform joint weak measurements on post-selected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here, we experimentally perform weak measurements of joint (i.e. nonlocal) observables. In an implementation of Hardy's Paradox, we weakly measure the locations of two photons, the subject of the conflicting statements behind the Paradox. Remarkably, the resulting weak probabilities verify all these statements but, at the same time, resolve the Paradox.

References in corpus (13)

• Quantum Mechanical Interaction-Free Measurements
• Quantum weak values
• Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values
• Experimental Realization of the Quantum Box Problem
• Driving non-Gaussian to Gaussian states with linear optics
• A double-slit `which-way' experiment on the complementarity--uncertainty debate
• Sequential weak measurement
• Extracting joint weak values with local, single-particle measurements
• A conditional-phase switch at the single-photon level
• Practical measurement of joint weak values and their connection to the annihilation operator
• Nonlinear optics with less than one photon
• Realisation of Hardy's Thought Experiment
• Counterfactual Statements and Weak Measurements: an Experimental Proposal

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