dorsal/arxiv
View SchemaRevisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values
| Authors | Yakir Aharonov, Alonso Botero, Sandu Popescu, Benni Reznik, Jeff Tollaksen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0104062 |
| URL | https://arxiv.org/abs/quant-ph/0104062 |
| DOI | 10.1016/S0375-9601(02)00986-6 |
Abstract
Classical-realistic analysis of entangled systems have lead to retrodiction paradoxes, which ordinarily have been dismissed on the grounds of counter-factuality. Instead, we claim that such paradoxes point to a deeper logical structure inherent to quantum mechanics, which is naturally described in the language of weak values, and which is accessible experimentally via weak measurements. Using as an illustration, a gedanken-experiment due to Hardy\cite{hardy}, we show that there is in fact an exact numerical coincidence between a) a pair of classically contradictory assertions about the locations of an electron and a positron, and b) the results of weak measurements of their location. The internal consistency of these results is due to the novel way by which quantum mechanics "resolves" the paradox: first, by allowing for two distinguishable manifestations of how the electron and positron can be at the same location: either as single particles or as a pair; and secondly, by allowing these properties to take either sign. In particular, we discuss the experimental meaning of a {\em negative} number of electron-positron pairs.
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"abstract": "Classical-realistic analysis of entangled systems have lead to retrodiction\nparadoxes, which ordinarily have been dismissed on the grounds of\ncounter-factuality. Instead, we claim that such paradoxes point to a deeper\nlogical structure inherent to quantum mechanics, which is naturally described\nin the language of weak values, and which is accessible experimentally via weak\nmeasurements. Using as an illustration, a gedanken-experiment due to\nHardy\\cite{hardy}, we show that there is in fact an exact numerical coincidence\nbetween a) a pair of classically contradictory assertions about the locations\nof an electron and a positron, and b) the results of weak measurements of their\nlocation. The internal consistency of these results is due to the novel way by\nwhich quantum mechanics \"resolves\" the paradox: first, by allowing for two\ndistinguishable manifestations of how the electron and positron can be at the\nsame location: either as single particles or as a pair; and secondly, by\nallowing these properties to take either sign. In particular, we discuss the\nexperimental meaning of a {\\em negative} number of electron-positron pairs.",
"arxiv_id": "quant-ph/0104062",
"authors": [
"Yakir Aharonov",
"Alonso Botero",
"Sandu Popescu",
"Benni Reznik",
"Jeff Tollaksen"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/S0375-9601(02)00986-6",
"title": "Revisiting Hardy\u0027s Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values",
"url": "https://arxiv.org/abs/quant-ph/0104062"
},
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