Paradoxical consequences of multipath coherence: perfect interaction-free measurements

Z. Zhao , S. Mondal , M. Markiewicz , Adam Rutkowski , B. Dakić , Wiesław Laskowski , T. Paterek

Abstract

Quantum coherence can be used to infer the presence of a detector without triggering it. Here we point out that, according to quantum mechanics, such interaction-free measurements cannot be perfect, i.e., in a single-shot experiment one has strictly positive probability to activate the detector. We formalize the extent to which such measurements are forbidden by deriving a trade-off relation between the probability of activation and the probability of an inconclusive interaction-free measurement. Our description of interaction-free measurements is theory independent and allows derivations of similar relations in models generalizing quantum mechanics. We provide the trade-off for the density cube formalism, which extends the quantum model by permitting coherence between more than two paths. The trade-off obtained hints at the possibility of perfect interaction-free measurements and indeed we construct their explicit examples. Such measurements open up a paradoxical possibility where we can learn by means of interference about the presence of an object in a given location without ever detecting a probing particle in that location. We therefore propose that absence of perfect interaction-free measurement is a natural postulate expected to hold in all physical theories. As shown, it holds in quantum mechanics and excludes the models with multipath coherence.
Author Z. Zhao
Z. Zhao,,
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, S. Mondal
S. Mondal,,
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, M. Markiewicz
M. Markiewicz,,
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, Adam Rutkowski (FMPI / ITPA)
Adam Rutkowski,,
- Institute of Theoretical Physics and Astrophysics
, B. Dakić
B. Dakić,,
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, Wiesław Laskowski (FMPI / ITPA)
Wiesław Laskowski,,
- Institute of Theoretical Physics and Astrophysics
, T. Paterek
T. Paterek,,
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Journal seriesPhysical Review A, ISSN 1050-2947, (A 35 pkt)
Issue year2018
Vol98
No2
Pages1-13
Publication size in sheets0.6
DOIDOI:10.1103/PhysRevA.98.022108
URL https://journals.aps.org/pra/pdf/10.1103/PhysRevA.98.022108
Languageen angielski
Score (nominal)35
ScoreMinisterial score = 35.0, 24-10-2018, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 24-10-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 2.925 (2) - 2016=2.716 (5)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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