Negative probabilities and Counterfactual Reasoning on the double-slit Experiment
arXiv:1412.4888
Abstract
In this paper we attempt to establish a theory of negative (quasi) probability distributions from fundamental principles and apply it to the study of the double-slit experiment in quantum mechanics. We do so in a way that preserves the main conceptual issues intact but allow for a clearer analysis, by representing the double-slit experiment in terms of the Mach-Zehnder interferometer, and show that the main features of quantum systems relevant to the double-slit are present also in the Mach-Zehnder. This converts the problem from a continuous to a discrete random variable representation. We then show that, for the Mach-Zehnder interferometer, negative probabilities do not exist that are consistent with interference and which-path information, contrary to what Feynman believed. However, consistent with Scully et al.'s experiment, if we reduce the amount of experimental information about the system and rely on counterfactual reasoning, a joint negative probability distribution can be constructed for the Mach-Zehnder experiment.
arXiv comment24 pages, 4 figures, submitted to a volume in honor of Patrick Suppes edited by Jean-Yves Beziau and Decio Krause
References in corpus (13)
- Contextuality supplies the magic for quantum computation
- Experimental realization of Wheeler's delayed-choice GedankenExperiment
- Condition for macroscopic realism beyond the Leggett-Garg inequalities
- Contextuality in Three Types of Quantum-Mechanical Systems
- All-Possible-Couplings Approach to Measuring Probabilistic Context
- Simulating all non-signalling correlations via classical or quantum theory with negative probabilities
- Unified approach to contextuality, non-locality, and temporal correlations
- Leggett-Garg Inequalities, Pilot Waves and Contextuality
- Interpretations of Negative Probabilities
- Generalizing Bell-type and Leggett-Garg-type Inequalities to Systems with Signaling
- A Collection of Probabilistic Hidden-Variable Theorems and Counterexamples
- Measuring Observable Quantum Contextuality
- The negative probabilities and information gain in weak measurements