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Fringe Visibility and Which-Way Information: An Inequality
Abstract
An inequality is derived according to which the fringe visibility in a two-way interferometer sets an absolute upper bound on the amount of which-way information that is potentially stored in a which-way detector. In some sense, this inequality can be regarded as quantifying the notion of wave-particle duality. The derivation of the inequality does not make use of Heisenberg's uncertainty relation in any form.
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“Remarkably, monogamy is manifested in the constraint of the energy distribution for the considered spin pair through a complementarity relation[46, 47]”
From Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems (2011) · cites this paper as [46]
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Cites
�ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
Heisenberg, W. (1927) · Zeitschrift f�r Physik · doi:10.1007/bf01397280 · Cited by 4,278
Robertson, H. P. (1929) · Physical Review · doi:10.1103/physrev.34.163 · Cited by 1,877
Albert Einstein: Philosopher-Scientist
Synge, J. L. (1950) · The Journal of Higher Education · doi:10.1080/00221546.1950.11776081 · Cited by 1,381
Quantum optical tests of complementarity
Scully, M. O., Englert, B., & WALTHER, H. (1991) · Nature · doi:10.1038/351111a0 · Cited by 852
Self-citationWootters, W. K., & Zurek, W. H. (1979) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.19.473 · Cited by 608
Simultaneous wave and particle knowledge in a neutron interferometer
Greenberger, D. M., & YA'SIN, A. (1988) · Physics Letters A · doi:10.1016/0375-9601(88)90114-4 · Cited by 454
Das Quantenpostulat und die neuere Entwicklung der Atomistik
Bohr, N. (1928) · Die Naturwissenschaften · doi:10.1007/bf01504968 · Cited by 252
Coherence and indistinguishability
Mandeļ, L. (1991) · Optics Letters · doi:10.1364/ol.16.001882 · Cited by 237
Stochastic and deterministic absorption in neutron-interference experiments
Summhammer, J., Rauch, H., & Tuppinger, D. (1987) · Physical Review A · doi:10.1103/physreva.36.4447 · Cited by 141
Static versus time-dependent absorption in neutron interferometry
Rauch, H., & Summhammer, J. (1984) · Physics Letters A · doi:10.1016/0375-9601(84)90586-3 · Cited by 84
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Research works printed but not linked: 1
- B.-G. Englert, 1996, Acta Phys. Slov., 46, 249
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Verma, H., Zych, M., & Costa, F. (2021) · Quantum · doi:10.22331/q-2021-08-17-525 · Cited by 2
“There exists a complementarity relation between path distinguishability (D) and interferometric visibility (V) [21, 22] which is given as follows:”
BackgroundComplete Complementarity Relations in System–environment Decoherent Dynamics
Basso, M. L. W., & Maziero, J. (2021) · Brazilian Journal of Physics · doi:10.1007/s13538-021-00931-6 · Cited by 3
“Later, this work was extended by Englert, who derived a wave-particle duality relation [5].”
MethodA probabilistic view of wave-particle duality for single photons
Aiello, A. (2023) · Quantum · doi:10.22331/q-2023-10-11-1135 · Cited by 3
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Chiou, D.-W., & Hsu, H.-C. (2024) · Quantum Information Processing · doi:10.1007/s11128-023-04214-8 · Cited by 3
“Originally, it was argued that the two principles are independent [4].”
Quantum Histories and Quantum Complementarity
Georgiev, D. D. (2012) · ISRN Mathematical Analysis · doi:10.5402/2012/327278 · Cited by 3
Phase-dependent which-way information
Schilling, U., & von Zanthier, J. (2012) · Physics Letters A · doi:10.1016/j.physleta.2012.10.019 · Cited by 3
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Elbaz, C. (2016) · Studies in Engineering and Technology · doi:10.11114/set.v3i1.1730 · Cited by 3
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Pennini, F., & Plastino, A. (2015) · Entropy · doi:10.3390/e17127853 · Cited by 3
Rameez‐ul‐Islam, Ikram, M., Mujtaba, A. H., & Abbas, T. (2017) · Laser Physics Letters · doi:10.1088/1612-202x/aa9826 · Cited by 3
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Sharma, G., Siddiqui, M. A., Mal, S., Sazim, S., & Sen, A. (2020) · Physics Letters A · doi:10.1016/j.physleta.2020.126297 · Cited by 3
“The path distinguishability characterizes the particle nature of the quanton and its quantifier can be written as [9, 16, 46]”
BackgroundInfluentialWave-particle duality using the Compton effect
Pollyceno, L. D. S., & Ribeiro, A. D. (2020) · Physics Letters A · doi:10.1016/j.physleta.2020.126808 · Cited by 3
“For completeness, we should mention that other important contributions around the theme were developed as, for instance, a necessary formalism in order to quantify wave and corpuscular behaviors [15, 16, 17] or a study involving a possible application to general relativity [18, 19].”
BackgroundInterference of the scattered vector light fields from two optically levitated nanoparticles
Jin, Y., Yan, J., Rahman, S. J., Yu, X., & Zhang, J. (2022) · Optics Express · doi:10.1364/oe.454082 · Cited by 3
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Jara, M., Marrou, J. P., Uria, M., Torre, C. M. L., & Zela, F. D. (2022) · Optics Express · doi:10.1364/oe.466010 · Cited by 3
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“[12] B.-G. Englert, Fringe visibility and which-way information: An inequality, Phys.”
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dos Santos, A. F., Barbosa, N. E. L., Ferreira, J. L. M., & Bernardo, B. D. L. (2023) · Quantum Information Processing · doi:10.1007/s11128-022-03813-1 · Cited by 3
“[4, 5], in which only the influence of the path probability is considered.”
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Halder, A., & Friberg, A. T. (2019) · Optics Letters · doi:10.1364/ol.45.000192 · Cited by 3
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Tanimura, S. (2015) · Quanta · doi:10.12743/quanta.v4i1.35 · Cited by 6
“Englert [38] formulated a qualitative relation between distinguishability and interference visibility.”
BackgroundThree-slit ghost interference and non-local duality
Siddiqui, M. A. (2015) · International Journal of Quantum Information · doi:10.1142/s0219749915500227 · Cited by 3
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Nambu, Y., Tomita, A., Chiba-Kohno, Y., & Nakamura, K. T. (2000) · Physical Review A · doi:10.1103/physreva.62.012312 · Cited by 3
Coherence loss and revivals in atomic interferometry: a quantum-recoil analysis
Davidović, M., Sanz, Á. S., Božić, M., & Arsenović, D. (2012) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/45/16/165303 · Cited by 3
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Cañizares, P., Görler, T., Paz, J. P., Morigi, G., & Schleich, W. P. (2007) · Laser Physics · doi:10.1134/s1054660x0707002x · Cited by 3
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“A only (as in Fig. (1) ). When there is no a priori bias toward either path (P = 0), but there is a WW detector, Eq. (1) applies with D = E = 1 2 Tr ρa D − ρ b D . (10) Here E is the detector efficiency[5] expressed as the trace norm of the difference of the two detector states (the absolute value of an operator, O, is d…”
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BackgroundMethodResultInfluentialTheory of interaction-free measurements in cavity resonators
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(2006) · Duke University Press eBooks · doi:10.1215/9780822388128-006 · Cited by 6
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“(1) [7].”
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BackgroundLiu, Z., Zhu, C., Yin, H., & Wang, X. (2025) · Physical Review A · doi:10.1103/physreva.111.062215 · Cited by 2
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“[3] Berthold-Georg Englert, “Fringe Visibility and WhichWay Information: An Inequality,” Phys.”
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Bandyopadhyay, S. (2012) · Springer eBooks · doi:10.1007/978-1-4614-1141-3_8 · Cited by 1
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“(III.14) turns into the duality relation presented in [21].”
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Jakob, M. (2026) · Optics Communications · doi:10.1016/j.optcom.2026.133544 · Cited by 1
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Kwiat, P. G. (2009) · Springer eBooks · doi:10.1007/978-3-540-70626-7_131 · Cited by 1
Metadata
- Authors
- Englert, B.-G.
- Affiliations
- Max Planck Institute of Quantum Optics (DE)
- Corresponding author
- Englert, Berthold-Georg
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1996-09-09
- Volume
- 77
- Issue
- 11
- Pages
- 2154-2157
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2156583743
- Cited by
- 821
- References
- 12
- Citations by year
- 2026: 38 · 2025: 41 · 2024: 34 · 2023: 33 · 2022: 40 · 2021: 51 · 2020: 35 · 2019: 43 · 2018: 38 · 2017: 40 · 2016: 36 · 2015: 42 · 2014: 36 · 2013: 18 · 2012: 29
- FWCI
- 5.51
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- fringe visibility, which-way information, wave-particle duality, information-theoretic inequalities, quantum interference, complementarity
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