Counterfactual Statements and Weak Measurements: an Experimental Proposal

Abstract

A recent analysis [quant-ph/0104062] suggests that weak measurements can be used to give observational meaning to counterfactual reasoning in quantum physics. A weak measurement is predicted to assign a negative unit population to a specific state in an interferometric Gedankenexperiment proposed by Hardy. We propose an experimental implementation with trapped ions of the Gedankenexperiment and of the weak measurement. In our standard quantum mechanical analysis of the proposal no states have negative population, but we identify the registration of a negative population by particles being displaced on average in the direction opposite to a force acting upon them.

References in corpus (2)

• Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values
• Multi-bit gates for quantum computing

Cited by in corpus (15)

• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Quantum weak values
• Experimental Realization of the Quantum Box Problem
• Precision metrology using weak measurements
• A double-slit `which-way' experiment on the complementarity--uncertainty debate
• Extracting joint weak values with local, single-particle measurements
• Quantum Non-demolition Measurements on Qubits
• Practical measurement of joint weak values and their connection to the annihilation operator
• Weak Values with Decoherence
• Weak measurements with a qubit meter
• Experimental realization of post-selected weak measurements on an NMR quantum processor
• Reconstructing weak values without weak measurements
• Quantum uncertainty as classical uncertainty of real-deterministic variables constructed from complex weak values and a global random variable
• Comment on "A linear optics implementation of weak values in Hardy's paradox"
• Testing Bell inequalities with weak measurements