dorsal/arxiv
View SchemaComplementarity and Uncertainty in Mach-Zehnder Interferometry and beyond
| Authors | Paul Busch, Christopher R. Shilladay |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609048 |
| URL | https://arxiv.org/abs/quant-ph/0609048 |
| DOI | 10.1016/j.physrep.2006.09.001 |
| Journal | Physics Reports 435 (2006) 1-31 |
Abstract
A coherent account of the connections and contrasts between the principles of com- plementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by means of a set of experimental schemes based on Mach-Zehnder interferometry. In particu- lar, path detection via entanglement with a probe system and (quantitative) quan- tum erasure are exhibited to constitute instances of joint unsharp measurements of complementary pairs of physical quantities, path and interference observables. The analysis uses the representation of observables as positive-operator-valued measures (POVMs). The reconciliation of complementary experimental options in the sense of simultaneous unsharp preparations and measurements is expressed in terms of uncertainty relations of different kinds. The feature of complementarity, manifest in the present examples in the mutual exclusivity of path detection and interference observation, is recovered as a limit case from the appropriate uncertainty relation. It is noted that the complementarity and uncertainty principles are neither completely logically independent nor logical consequences of one another. Since entanglement is an instance of the uncertainty of quantum properties (of compound systems), it is moot to play out uncertainty and entanglement against each other as possible mechanisms enforcing complementarity.
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"abstract": "A coherent account of the connections and contrasts between the principles of\ncom- plementarity and uncertainty is developed starting from a survey of the\nvarious formalizations of these principles. The conceptual analysis is\nillustrated by means of a set of experimental schemes based on Mach-Zehnder\ninterferometry. In particu- lar, path detection via entanglement with a probe\nsystem and (quantitative) quan- tum erasure are exhibited to constitute\ninstances of joint unsharp measurements of complementary pairs of physical\nquantities, path and interference observables. The analysis uses the\nrepresentation of observables as positive-operator-valued measures (POVMs). The\nreconciliation of complementary experimental options in the sense of\nsimultaneous unsharp preparations and measurements is expressed in terms of\nuncertainty relations of different kinds. The feature of complementarity,\nmanifest in the present examples in the mutual exclusivity of path detection\nand interference observation, is recovered as a limit case from the appropriate\nuncertainty relation. It is noted that the complementarity and uncertainty\nprinciples are neither completely logically independent nor logical\nconsequences of one another. Since entanglement is an instance of the\nuncertainty of quantum properties (of compound systems), it is moot to play out\nuncertainty and entanglement against each other as possible mechanisms\nenforcing complementarity.",
"arxiv_id": "quant-ph/0609048",
"authors": [
"Paul Busch",
"Christopher R. Shilladay"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.physrep.2006.09.001",
"journal_ref": "Physics Reports 435 (2006) 1-31",
"title": "Complementarity and Uncertainty in Mach-Zehnder Interferometry and beyond",
"url": "https://arxiv.org/abs/quant-ph/0609048"
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