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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Monogamy is manifested in a complementarity relation that restricts the maximal amount of energy or entanglement associated with correlated spin systems.
“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]
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 · see citing works
Robertson, H. P. (1929) · Physical Review · doi:10.1103/physrev.34.163 · Cited by 1,877 · see citing works
Albert Einstein: Philosopher-Scientist
Synge, J. L. (1950) · The Journal of Higher Education · doi:10.1080/00221546.1950.11776081 · Cited by 1,352 · see citing works
Quantum optical tests of complementarity
Scully, M. O., Englert, B., & WALTHER, H. (1991) · Nature · doi:10.1038/351111a0 · Cited by 861 · see citing works
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 · see citing works
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 · see citing works
Das Quantenpostulat und die neuere Entwicklung der Atomistik
Bohr, N. (1928) · Die Naturwissenschaften · doi:10.1007/bf01504968 · Cited by 252 · see citing works
Coherence and indistinguishability
Mandeļ, L. (1991) · Optics Letters · doi:10.1364/ol.16.001882 · Cited by 237 · see citing works
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 · see citing works
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 · see citing works
Quantum optical ramsey fringes and complementarity
Englert, B., WALTHER, H., & Scully, M. O. (1992) · Applied Physics B · doi:10.1007/bf00325381 · Cited by 41 · see citing works
Self-citationLévy-Leblond, J.-M. (1988) · Physica B+C · doi:10.1016/0378-4363(88)90185-4 · Cited by 24 · see citing works
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(2007) · Project Muse (Johns Hopkins University) · Cited by 7,214 · see citing works
Optics and interferometry with atoms and molecules
Cronin, A. D., Schmiedmayer, J., & Pritchard, D. E. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.1051 · Cited by 1,427 · see citing works
“, 1995) and (Englert, 1996) to quantify how much ‘which-path’ knowledge (K) can be obtained and how much contrast (C) can be observed at the output of an interferometer.”
BackgroundDurt, T., Englert, B., Bengtsson, I., & Życzkowski, K. (2010) · International Journal of Quantum Information · doi:10.1142/s0219749910006502 · Cited by 715 · see citing works
Self-citationEntropic uncertainty relations and their applications
Coles, P. J., Berta, M., Tomamichel, M., & Wehner, S. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.015002 · Cited by 668 · see citing works
Caruso, F., Chin, A. W., Datta, A., Huelga, S. F., & Plenio, M. B. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3223548 · Cited by 655 · see citing works
Getting Real: Technoscientific Practices and the Materialization of Reality
Barad, K. (1998) · differences · doi:10.1215/10407391-10-2-87 · Cited by 606 · see citing works
Experimental Realization of Wheeler's Delayed-Choice Gedanken Experiment
Jacques, V., Wu, E., Grosshans, F., Treussart, F., Grangier, P., Aspect, A., & Roch, J.-F. (2007) · Science · doi:10.1126/science.1136303 · Cited by 569 · see citing works
Dephasing in electron interference by a ‘which-path’ detector
Buks, E., Schuster, R., Heiblum, M., Mahalu, D., & Umansky, V. (1998) · Nature · doi:10.1038/36057 · Cited by 506 · see citing works
Schlosshauer, M. (2019) · Physics Reports · doi:10.1016/j.physrep.2019.10.001 · Cited by 521 · see citing works
“In fact, there is a continuous tradeoff between interference (phase information) and which-path information: the better we can distinguish the two possible paths, the less visible the interference pattern becomes [44, 45].”
BackgroundQuantum coherence and geometric quantum discord
Hu, M., Hu, X., Wang, J., Peng, Y., Zhang, Y.-R., & Fan, H. (2018) · Physics Reports · doi:10.1016/j.physrep.2018.07.004 · Cited by 434 · see citing works
“(340), i.e., C2 l1 (ρ′s) (N − 1)2 +D 2 ≤ 1, (341) which is similar to the complementarity relationD2 +V2 ≤ 1 given by Englert (1996).”
BackgroundOperationally Invariant Information in Quantum Measurements
Brukner, Č., & Zeilinger, A. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.3354 · Cited by 311 · see citing works
Walborn, S. P., Cunha, M. T., Pádua, S., & Monken, C. H. (2002) · Physical Review A · doi:10.1103/physreva.65.033818 · Cited by 308 · see citing works
Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
Hillery, M. S. (2016) · Physical Review A · doi:10.1103/physreva.93.012111 · Cited by 278 · see citing works
Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
Yokota, K., Yamamoto, T., Koashi, M., & Imoto, N. (2009) · New Journal of Physics · doi:10.1088/1367-2630/11/3/033011 · Cited by 272 · see citing works
Physics with the KLOE-2 experiment at the upgraded DAΦNE
Giovanni Amelino-camelia, A., Archilli, F., Babusci, D., Badoni, D., Bencivenni, G., Bernabéu, J., Bertlmann, R. A., Boito, D., Bini, C., Bloise, C., et al. (2010) · The European Physical Journal C · doi:10.1140/epjc/s10052-010-1351-1 · Cited by 283 · see citing works
A Quantum Delayed-Choice Experiment
Peruzzo, A., Shadbolt, P., Brunner, N., Popescu, S., & O’Brien, J. L. (2012) · Science · doi:10.1126/science.1226719 · Cited by 265 · see citing works
“This is the notion of complementarity in quantum mechanics [4, 5], which is central in the stan-”
BackgroundDuality of quantum coherence and path distinguishability
Bera, M. N., Qureshi, T., Siddiqui, M. A., & Pati, A. K. (2015) · Physical Review A · doi:10.1103/physreva.92.012118 · Cited by 255 · see citing works
Quantum interferometric visibility as a witness of general relativistic proper time
Zych, M., Costa, F., Pikovski, I., & Brukner, Č. (2011) · Nature Communications · doi:10.1038/ncomms1498 · Cited by 251 · see citing works
“The distinguishability D of the trajectories is the probability to correctly guess which path was taken in the two-way interferometer by measuring the degrees of freedom that serve as a which-way detector [12] (in mathematical terms it is the trace norm distance between the final states of the detectors associated wit…”
BackgroundSalles, A., de Melo, F., de Almeida, M. P., Hor-Meyll, M. O., Walborn, S. P., Ribeiro, P. H. S., & Davidovich, L. (2008) · Physical Review A · doi:10.1103/physreva.78.022322 · Cited by 251 · see citing works
Delayed-choice gedanken experiments and their realizations
Ma, X., Kofler, J., & Zeilinger, A. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.015005 · Cited by 222 · see citing works
“(14) (Wootters and Zurek, 1979; Greenberger and Yasin, 1988; Jaeger, Shimony, and Vaidman, 1995; Englert, 1996), in which D and V stand for conditional which-path information (distinguishability) and interference visibilities, respectively.”
BackgroundRelations between Coherence and Path Information
Bagán, E., Bergou, J. A., Cottrell, S. S., & Hillery, M. S. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.160406 · Cited by 220 · see citing works
Quantum discord and its allies: a review of recent progress
Bera, A., Das, T., Sadhukhan, D., Roy, S. S., Sen, A., & Sen, U. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa872f · Cited by 221 · see citing works
“A 53 2038 [31] Englert B G 1996 Fringe Visibility and Which-Way In-”
BackgroundA complementarity experiment with an interferometer at the quantum–classical boundary
Bertet, P., Osnaghi, S., Rauschenbeutel, A., Nogues, G., Auffèves, A., Brune, M., Raimond, J. M., & Haroche, S. (2001) · Nature · doi:10.1038/35075517 · Cited by 212 · see citing works
Fringe Visibility and Which-Way Information in an Atom Interferometer
Dürr, S., Nonn, T., & Rempe, G. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.5705 · Cited by 205 · see citing works
Entanglement-Enabled Delayed-Choice Experiment
Kaiser, F., Coudreau, T., Milman, P., Ostrowsky, D. B., & Tanzilli, S. (2012) · Science · doi:10.1126/science.1226755 · Cited by 199 · see citing works
Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems
Ma, X.-S., Dakic, B., Naylor, W., Zeilinger, A., & Walther, P. (2011) · Nature Physics · doi:10.1038/nphys1919 · Cited by 179 · see citing works
“Remarkably, monogamy is manifested in the constraint of the energy distribution for the considered spin pair through a complementarity relatio”
BackgroundQuantum Optical Technologies for Metrology, Sensing, and Imaging
Dowling, J. P., & Seshadreesan, K. P. (2014) · Journal of Lightwave Technology · doi:10.1109/jlt.2014.2386795 · Cited by 178 · see citing works
“In the above, it is possible to get rid of the dependence on the actual value of phase by considering the fringe visibility observable [55].”
BackgroundProposal for a Quantum Delayed-Choice Experiment
Ionicioiu, R., & Terno, D. R. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.230406 · Cited by 173 · see citing works
Quantitative wave-particle duality and nonerasing quantum erasure
Schwindt, P. D. D., Kwiat, P. G., & Englert, B. (1999) · Physical Review A · doi:10.1103/physreva.60.4285 · Cited by 156 · see citing works
Self-citationDelayed-Choice Test of Quantum Complementarity with Interfering Single Photons
Jacques, V., Wu, E., Grosshans, F., Treussart, F., Grangier, P., Aspect, A., & Roch, J.-F. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.220402 · Cited by 158 · see citing works
Wheeler's delayed-choice gedanken experiment with a single atom
Manning, A., Khakimov, R. I., Dall, R. G., & Truscott, A. G. (2015) · Nature Physics · doi:10.1038/nphys3343 · Cited by 148 · see citing works
Zeilinger, A., Weihs, G., Jennewein, T. D., & Aspelmeyer, M. (2005) · Nature · doi:10.1038/nature03280 · Cited by 142 · see citing works
Realization of quantum Wheeler's delayed-choice experiment
Tang, J., Li, Y., Xu, X., Xiang, G., Li, C., & Guo, G. (2012) · Nature Photonics · doi:10.1038/nphoton.2012.179 · Cited by 135 · see citing works
Sampling of partially distinguishable bosons and the relation to the multidimensional permanent
Tichy, M. C. (2015) · Physical Review A · doi:10.1103/physreva.91.022316 · Cited by 133 · see citing works
Measuring a Photonic Qubit without Destroying It
Pryde, G. J., O’Brien, J. L., White, A. G., Bartlett, S. D., & Ralph, T. C. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.190402 · Cited by 127 · see citing works
Quantitative wave-particle duality in multibeam interferometers
Dürr, S. (2001) · Physical Review A · doi:10.1103/physreva.64.042113 · Cited by 126 · see citing works
Quantitative complementarity relations in bipartite systems: Entanglement as a physical reality
Jakob, M., & Bergou, J. A. (2009) · Optics Communications · doi:10.1016/j.optcom.2009.10.044 · Cited by 125 · see citing works
Englert, B., & Bergou, J. A. (2000) · Optics Communications · doi:10.1016/s0030-4018(99)00718-x · Cited by 124 · see citing works
Self-citationInformation and Fundamental Elements of the Structure of Quantum Theory
Brukner, Č., & Zeilinger, A. (2003) · Springer eBooks · doi:10.1007/978-3-662-10557-3_21 · Cited by 122 · see citing works
Localization and loss of coherence in molecular double-slit experiments
Zimmermann, B., Rolles, D., Langer, B., Hentges, R., Braune, M., Cvejanović, S., Geßner, O., Heiser, F., Korica, S., Lischke, T., et al. (2008) · Nature Physics · doi:10.1038/nphys993 · Cited by 122 · see citing works
“Such interactions reduce the interference contrast and eventually provide ‘which way’ informatio”
BackgroundElectromagnetic theory of optical coherence [Invited]
Friberg, A. T., & Setälä, T. (2016) · Journal of the Optical Society of America A · doi:10.1364/josaa.33.002431 · Cited by 120 · see citing works
General relativistic effects in quantum interference of photons
Zych, M., Costa, F., Pikovski, I., Ralph, T. C., & Brukner, Č. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/22/224010 · Cited by 117 · see citing works
“If we quantify the amount of the which-way information D (distinguishability of the trajectories) as the probability to correctly guess which path was taken in the two-way interferometer [10], we obtain D = √ 1 − |〈τ1|τ2〉|2.”
BackgroundMethodEquivalence of wave–particle duality to entropic uncertainty
Coles, P. J., Kaniewski, J., & Wehner, S. (2014) · Nature Communications · doi:10.1038/ncomms6814 · Cited by 115 · see citing works
Theory of quantum imaging with undetected photons
Lahiri, M., Łapkiewicz, R., Lemos, G. B., & Zeilinger, A. (2015) · Physical Review A · doi:10.1103/physreva.92.013832 · Cited by 114 · see citing works
Quantum erasure with causally disconnected choice
Ma, X., Kofler, J., Qarry, A., Tetik, N., Scheidl, T., Ursin, R., Ramelow, S., Herbst, T., Ratschbacher, L., Fedrizzi, A., et al. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1213201110 · Cited by 118 · see citing works
“To quantitatively demonstrate the quantum eraser and the complementarity principle under Einstein locality, we use a bipartite complementarity inequality (22, 47, 48), namely,”
MethodProgress in electron- and ion-interferometry
HASSELBACH, F. (2009) · Reports on Progress in Physics · doi:10.1088/0034-4885/73/1/016101 · Cited by 112 · see citing works
The Uncertainty Relations in Quantum Mechanics
Sen, D. (2014) · doi:10.18520/cs/v107/i2/203-218 · Cited by 112 · see citing works
Partial indistinguishability theory for multiphoton experiments in multiport devices
Shchesnovich, V. S. (2015) · Physical Review A · doi:10.1103/physreva.91.013844 · Cited by 108 · see citing works
Generic Entanglement Generation, Quantum Statistics, and Complementarity
Bose, S., & Home, D. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.050401 · Cited by 111 · see citing works
WAVE-PARTICLE DUALITY IN MULTI-PATH INTERFEROMETERS: GENERAL CONCEPTS AND THREE-PATH INTERFEROMETERS
Englert, B., Kaszlikowski, D., Kwek, L. C., & Chee, W. H. (2008) · International Journal of Quantum Information · doi:10.1142/s0219749908003220 · Cited by 110 · see citing works
Self-citationCoherence and complementarity in state-channel interaction
Luo, S., & Sun, Y. (2018) · Physical Review A · doi:10.1103/physreva.98.012113 · Cited by 109 · see citing works
Quantum‐Memory‐Assisted Entropic Uncertainty Relations
Wang, D., Ming, F., Hu, M., & Ye, L. (2019) · Annalen der Physik · doi:10.1002/andp.201900124 · Cited by 98 · see citing works
Quantum concepts in optical polarization
Goldberg, A. Z., de la Hoz, P., Bjork, G. G., Klimov, A. B., Grassl, M., Leuchs, G., & Sánchez-Soto, L. L. (2020) · Advances in Optics and Photonics · doi:10.1364/aop.404175 · Cited by 98 · see citing works
Suzuki, Y., Iinuma, M., & Hofmann, H. F. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/10/103022 · Cited by 97 · see citing works
Quantum nondemolition measurements for quantum information
Ralph, T. C., Bartlett, S. D., O’Brien, J. L., Pryde, G. J., & Wiseman, H. M. (2006) · Physical Review A · doi:10.1103/physreva.73.012113 · Cited by 92 · see citing works
Information Invariance and Quantum Probabilities
Brukner, Č., & Zeilinger, A. (2009) · Foundations of Physics · doi:10.1007/s10701-009-9316-7 · Cited by 94 · see citing works
“It does not only compromise the extreme cases of maximal knowledge of path information at the expense of complete loss of interference and vice versa, but also intermediate situations in which one can obtain some partial knowledge about the particle’s path and still observe an interference pattern of reduced contrast…”
BackgroundEntanglement limits duality and vice versa
Qian, X., Vamivakas, A. N., & Eberly, J. H. (2018) · Optica · doi:10.1364/optica.5.000942 · Cited by 91 · see citing works
A self-interfering clock as a “which path” witness
Margalit, Y., Zhou, Z., Machluf, S., Rohrlich, D., Japha, Y., & Folman, R. (2015) · Science · doi:10.1126/science.aac6498 · Cited by 91 · see citing works
Joint measurement of two unsharp observables of a qubit
Yu, S., Liu, N.-L., Li, L., & Oh, C. H. (2010) · Physical Review A · doi:10.1103/physreva.81.062116 · Cited by 90 · see citing works
Quantum indistinguishability by path identity and with undetected photons
Hochrainer, A., Lahiri, M., Erhard, M., Krenn, M., & Zeilinger, A. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.025007 · Cited by 91 · see citing works
“[55] Berthold-Georg Englert, “Fringe visibility and whichway information: An inequality,” Physical Review Letters 77, 2154 (1996).”
BackgroundComplementarity and entanglement in bipartite qudit systems
Jakob, M., & Bergou, J. A. (2007) · Physical Review A · doi:10.1103/physreva.76.052107 · Cited by 88 · see citing works
Uncertainty relation revisited from quantum estimation theory
Watanabe, Y., Sagawa, T., & Ueda, M. (2011) · Physical Review A · doi:10.1103/physreva.84.042121 · Cited by 86 · see citing works
The Monge metric on the sphere and geometry of quantum states
Życzkowski, K., & Słomczyński, W. (2001) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/34/34/311 · Cited by 85 · see citing works
Paradox in Wave-Particle Duality
Afshar, S. S., Flores, E. V., McDonald, K., & Knoesel, E. (2007) · Foundations of Physics · doi:10.1007/s10701-006-9102-8 · Cited by 84 · see citing works
Interferometric visibility and coherence
Biswas, T., Díaz, M. G., & Winter, A. (2017) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2017.0170 · Cited by 79 · see citing works
Nonmonotonic quantum-to-classical transition in multiparticle interference
Ra, Y.-S., Tichy, M. C., Lim, H., Kwon, O., Mintert, F., Buchleitner, A., & Kim, Y.-H. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1206910110 · Cited by 77 · see citing works
Overcoming loss of contrast in atom interferometry due to gravity gradients
Roura, A., Zeller, W., & Schleich, W. P. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/12/123012 · Cited by 77 · see citing works
Experimental analysis of the quantum complementarity principle
Auccaise, R., Serra, R. M., Filgueiras, J. G., Sarthour, R. S., Oliveira, I. S., & Céleri, L. C. (2012) · Physical Review A · doi:10.1103/physreva.85.032121 · Cited by 73 · see citing works
Wave–Particle Duality: An Information-Based Approach
Angelo, R. M., & Ribeiro, A. D. (2015) · Foundations of Physics · doi:10.1007/s10701-015-9913-6 · Cited by 75 · see citing works
“Finally, we point out that like Englert’s approach [20], ours admits both the fundamental role of an informer and the occurrence of morphing behavior (here signalized when Iw > 0 and Ip > 0 simultaneously).”
BackgroundMethodResultRealization of a Minimal Disturbance Quantum Measurement
Sciarrino, F., Ricci, M., Martini, F. D., Filip, R., & Mišta, L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.020408 · Cited by 75 · see citing works
Entanglement, Bell Inequalities and Decoherence in Particle Physics
Bertlmann, R. A. (2006) · Springer eBooks · doi:10.1007/11398448_1 · Cited by 70 · see citing works
Quantum Marking and Quantum Erasure for Neutral Kaons
Bramòn, A., Garbarino, G., & Hiesmayr, B. C. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.020405 · Cited by 69 · see citing works
Experimental Progress on Quantum Coherence: Detection, Quantification, and Manipulation
Wu, K., Streltsov, A., Regula, B., Xiang, G., Li, C., & Guo, G. (2021) · Advanced Quantum Technologies · doi:10.1002/qute.202100040 · Cited by 66 · see citing works
Engineering Nonlinear Optic Sources of Photonic Entanglement
Torres, J. P., Banaszek, K., & Walmsley, I. A. (2011) · Progress in optics · doi:10.1016/b978-0-444-53886-4.00005-8 · Cited by 66 · see citing works
Coherence, polarization, and entanglement for classical light fields
Luis, A. (2009) · Optics Communications · doi:10.1016/j.optcom.2009.06.024 · Cited by 67 · see citing works
Quantitative complementarity in two-path interferometry
Bramòn, A., Garbarino, G., & Hiesmayr, B. C. (2004) · Physical Review A · doi:10.1103/physreva.69.022112 · Cited by 66 · see citing works
Complementarity and quantum walks
Kendon, V. M., & Sanders, B. C. (2005) · Physical Review A · doi:10.1103/physreva.71.022307 · Cited by 65 · see citing works
Can wave–particle duality be based on the uncertainty relation?
Dürr, S., & Rempe, G. (2000) · American Journal of Physics · doi:10.1119/1.1285869 · Cited by 66 · see citing works
Entropic framework for wave-particle duality in multipath interferometers
Coles, P. J. (2016) · Physical Review A · doi:10.1103/physreva.93.062111 · Cited by 65 · see citing works
“[5] Scully, M. O., Englert, B.-G. & Walther, H. Quantum optical tests of complementarity.”
BackgroundMethodInfluentialDisorder and interference: localization phenomena
Müller, C. A., & Delande, D. (2011) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199603657.003.0009 · Cited by 69 · see citing works
“A quantitative measure of this waveparticle-duality, developed originally in the context of Mach-Zehnder-type interferometers [86], can be investigated analytically in the simplest cases and highlights the rôle of which-path information in the loss of CBS interference visibility [87].”
BackgroundWitnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases
Hiesmayr, B. C., & Moskal, P. (2019) · Scientific Reports · doi:10.1038/s41598-019-44570-z · Cited by 61 · see citing works
Illustration of quantum complementarity using single photons interfering on a grating
Jacques, V., Lai, N. D., Dréau, A., Zheng, D., Chauvat, D., Treussart, F., Grangier, P., & Roch, J.-F. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/12/123009 · Cited by 59 · see citing works
“which puts an upper bound to the maximum values of independently determined interference visibility V and path distinguishability D, the parameter that quantifies the available WPI on the quantum system [ 4 ].”
BackgroundInfluentialAchieving quantum precision limit in adaptive qubit state tomography
Hou, Z., Zhu, H., Xiang, G., Li, C., & Guo, G. (2016) · npj Quantum Information · doi:10.1038/npjqi.2016.1 · Cited by 58 · see citing works
“A vivid manifestation of such tradeoff is the wave-particle duality relation between fringe visibility V and path distinguishability D [23, 24],”
BackgroundQuantum Interference Enforced by Time-Energy Complementarity
Kiffner, M., Evers, J., & Keitel, C. H. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.100403 · Cited by 57 · see citing works
Quantification of complementarity in multiqubit systems
Peng, X., Zhu, X., Suter, D., Du, J., Liu, M., & Gao, K. (2005) · Physical Review A · doi:10.1103/physreva.72.052109 · Cited by 56 · see citing works
Complementarity and the uncertainty relations
Bjork, G. G., Söderholm, J., Trifonov, A. S., Tsegaye, T., & Karlsson, A. (1999) · Physical Review A · doi:10.1103/physreva.60.1874 · Cited by 56 · see citing works
Complementarity and quantum erasure inwelcher Wegexperiments
Bjork, G. G., & Karlsson, A. (1998) · Physical Review A · doi:10.1103/physreva.58.3477 · Cited by 56 · see citing works
Quantum imaging and metrology with undetected photons: tutorial
Lemos, G. B., Lahiri, M., Ramelow, S., Łapkiewicz, R., & Plick, W. N. (2022) · Journal of the Optical Society of America B · doi:10.1364/josab.456778 · Cited by 55 · see citing works
Wave-particle dualism and complementarity unraveled by a different mode
Menzel, R., Puhlmann, D., Heuer, A., & Schleich, W. P. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1201271109 · Cited by 59 · see citing works
Quantum state discrimination: A geometric approach
Markham, D., Miszczak, J. A., Puchała, Z., & Życzkowski, K. (2008) · Physical Review A · doi:10.1103/physreva.77.042111 · Cited by 55 · see citing works
“In [14] Englert introduced the notion of distinguishability between two quantum states and showed that it is equal to the trace distance between them.”
BackgroundQian, X.-F., Konthasinghe, K., Manikandan, S. K., Spiecker, D., Vamivakas, A. N., & Eberly, J. H. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.012016 · Cited by 54 · see citing works
“[7] B.”
BackgroundInformation-Disturbance Tradeoff in Estimating a Maximally Entangled State
Sacchi, M. F. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.220502 · Cited by 54 · see citing works
Past of a quantum particle revisited
Englert, B., Horia, K., Dai, J., Len, Y. L., & Ng, H. K. (2017) · Physical Review A · doi:10.1103/physreva.96.022126 · Cited by 53 · see citing works
Self-citationFamily of coherence measures and duality between quantum coherence and path distinguishability
Xiong, C., Kumar, A., & Wu, J. (2018) · Physical Review A · doi:10.1103/physreva.98.032324 · Cited by 53 · see citing works
Quantum speed limits and optimal Hamiltonians for driven systems in mixed states
Andersson, O., & Heydari, H. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/21/215301 · Cited by 49 · see citing works
“ncertainty of the system. Uhlmann [15] showed that the same inequality holds for mixed states when orthogonality is replaced by distinguishability, which means that the fidelity of the states vanishes [28, 29]. To be precise, Uhlmann showed that if ρis a solution to (20), then the Bureslengthbetweentheinitialandfinalsta…”
BackgroundQuantum measurements and new concepts for experiments with trapped ionsPreprint
Wunderlich, C., & Balzer, C. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0305129 · Cited by 51 · see citing works
“A general quantitative relation between the amount of welcher weg information stored in a detector and the visibility of interference fringes has been given in (Englert 1996).”
Information complementarity: A new paradigm for decoding quantum incompatibility
Zhu, H. (2015) · Scientific Reports · doi:10.1038/srep14317 · Cited by 50 · see citing works
Induced Coherence, Vacuum Fields, and Complementarity in Biphoton Generation
Heuer, A., Menzel, R. W., & Milonni, P. W. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.053601 · Cited by 50 · see citing works
Duality Games and Operational Duality Relations
Bagán, E., Calsamiglia, J., Bergou, J. A., & Hillery, M. S. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.050402 · Cited by 50 · see citing works
Study of coherence and mixedness in meson and neutrino systems
Dixit, K., Naikoo, J., Banerjee, S., & Alok, A. K. (2019) · The European Physical Journal C · doi:10.1140/epjc/s10052-019-6609-7 · Cited by 50 · see citing works
- 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 › Computer Science › Artificial Intelligence › 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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