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Rebufello E, Piacentini F, Avella A, Souza MAD, Gramegna M, Dziewior J, Cohen E, Vaidman L, Degiovanni IP, Genovese M. Anomalous weak values via a single photon detection. LIGHT, SCIENCE & APPLICATIONS 2021; 10:106. [PMID: 34035219 PMCID: PMC8149841 DOI: 10.1038/s41377-021-00539-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Revised: 04/07/2021] [Accepted: 04/19/2021] [Indexed: 06/12/2023]
Abstract
Is it possible that a measurement of a spin component of a spin-1/2 particle yields the value 100? In 1988 Aharonov, Albert and Vaidman argued that upon pre- and postselection of particular spin states, weakening the coupling of a standard measurement procedure ensures this paradoxical result1. This theoretical prediction, called weak value, was realised in numerous experiments2-9, but its meaning remains very controversial10-19, since its "anomalous" nature, i.e., the possibility to exceed the eigenvalue spectrum, as well as its "quantumness" are debated20-22. We address these questions by presenting the first experiment measuring anomalous weak values with just a single click, without the need for statistical averaging. The measurement uncertainty is significantly smaller than the gap between the measured weak value and the nearest eigenvalue. Beyond clarifying the meaning of weak values, demonstrating their non-statistical, single-particle nature, this result represents a breakthrough in understanding the foundations of quantum measurement, showing unprecedented measurement capability for further applications of weak values to quantum photonics.
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Affiliation(s)
| | | | | | - Muriel A de Souza
- National Institute of Metrology, Quality and Technology-INMETRO, Av. Nossa Senhora das Graças, 50, Duque de Caxias, RJ, 25250-020, Brazil
| | | | - Jan Dziewior
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748, Garching, Germany
- Department für Physik, Ludwig-Maximilians-Universität, 80797, München, Germany
| | - Eliahu Cohen
- Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan, 5290002, Israel
| | - Lev Vaidman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv, 6997801, Israel
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2
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Aharonov Y, Cohen E, Carmi A, Elitzur AC. Extraordinary interactions between light and matter determined by anomalous weak values. Proc Math Phys Eng Sci 2018. [DOI: 10.1098/rspa.2018.0030] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Some predictions regarding pre- and post-selected states are far-reaching, thereby requiring validation with standard quantum measurements in addition to the customary weak measurements used so far, as well as other advanced techniques. We go further pursuing this goal, proposing two thought experiments which incorporate novel yet feasible validation methods of unconventional light-matter interactions. An excited atom traverses a Mach–Zehnder interferometer (MZI) under a special combination of pre- and post-selection. In the first experiment, photons emitted by the superposed atom, after being hit by two laser beams, are individually counted. Despite the interaction having definitely taken place, as revealed by the atom becoming ground, the numbers of photons emitted from each arm of the MZI are predicted, at the ensemble level, to be different from those expected with standard stimulated emission. In the second experiment, the atom spontaneously emits a photon while still in the MZI. This photon later serves as a strong measurement of the atom's energy upon hitting a photographic plate. The experiment is repeated to enable an interference effect of the emitted photons. Interestingly, the latter gives the appearance that the photons have been emitted by the atom from a position much farther from the two MZI arms
L
and
R
, as if in a ‘phantom arm’
R
′. Nevertheless, their time of arrival is similar to that of photons coming from
L
and
R
. These experiments also emphasize the key role of anomalous weak values in determining light–matter interactions. In fact, they present a straightforward realization of an entity we term counter-particles, namely pre- and post-selected states acting as if they have negative physical variables such as mass and energy. The novel verification methods we suggest for testing these predictions resemble weak measurements in some aspects, yet result from definite atomic transitions verified by the detected photons.
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Affiliation(s)
- Yakir Aharonov
- School of Physics and Astronomy, Tel Aviv University, Tel-Aviv 6997801, Israel
- Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA
- Schmid College of Science, Chapman University, Orange, CA 92866, USA
- Iyar, The Israeli Institute for Advanced Research, POB 651, Zichron Ya'akov 3095303, Israel
| | - Eliahu Cohen
- Iyar, The Israeli Institute for Advanced Research, POB 651, Zichron Ya'akov 3095303, Israel
- Physics Department, Centre for Research in Photonics, University of Ottawa, Advanced Research Complex, 25 Templeton, Ottawa, Ontario, Canada K1N 6N5
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK
| | - Avishy Carmi
- Iyar, The Israeli Institute for Advanced Research, POB 651, Zichron Ya'akov 3095303, Israel
- Center for Quantum Information Science and Technology and Faculty of Engineering Sciences Ben-Gurion University of the Negev, Beersheba 8410501, Israel
| | - Avshalom C. Elitzur
- Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA
- Iyar, The Israeli Institute for Advanced Research, POB 651, Zichron Ya'akov 3095303, Israel
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3
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Piacentini F, Avella A, Gramegna M, Lussana R, Villa F, Tosi A, Brida G, Degiovanni IP, Genovese M. Investigating the Effects of the Interaction Intensity in a Weak Measurement. Sci Rep 2018; 8:6959. [PMID: 29725051 PMCID: PMC5934410 DOI: 10.1038/s41598-018-25156-7] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2017] [Accepted: 04/13/2018] [Indexed: 11/09/2022] Open
Abstract
Measurements are crucial in quantum mechanics, for fundamental research as well as for applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. In the recent years, weak-interaction-based protocols like Weak Measurements and Protective Measurements have been experimentally realized, showing peculiar features leading to surprising advantages in several different applications. In this work we analyze the validity range for such measurement protocols, that is, how the interaction strength affects the weak value extraction, by measuring different polarization weak values on heralded single photons. We show that, even in the weak interaction regime, the coupling intensity limits the range of weak values achievable, setting a threshold on the signal amplification effect exploited in many weak measurement based experiments.
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Affiliation(s)
- Fabrizio Piacentini
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Alessio Avella
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Marco Gramegna
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Rudi Lussana
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Federica Villa
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Alberto Tosi
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Giorgio Brida
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Ivo Pietro Degiovanni
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Marco Genovese
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy.
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Direct quantum process tomography via measuring sequential weak values of incompatible observables. Nat Commun 2018; 9:192. [PMID: 29335489 PMCID: PMC5768737 DOI: 10.1038/s41467-017-02511-2] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2017] [Accepted: 12/06/2017] [Indexed: 11/09/2022] Open
Abstract
The weak value concept has enabled fundamental studies of quantum measurement and, recently, found potential applications in quantum and classical metrology. However, most weak value experiments reported to date do not require quantum mechanical descriptions, as they only exploit the classical wave nature of the physical systems. In this work, we demonstrate measurement of the sequential weak value of two incompatible observables by making use of two-photon quantum interference so that the results can only be explained quantum physically. We then demonstrate that the sequential weak value measurement can be used to perform direct quantum process tomography of a qubit channel. Our work not only demonstrates the quantum nature of weak values but also presents potential new applications of weak values in analyzing quantum channels and operations.
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Vaidman L. Weak value controversy. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2016.0395. [PMID: 28971947 PMCID: PMC5628259 DOI: 10.1098/rsta.2016.0395] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 05/30/2017] [Indexed: 06/07/2023]
Abstract
Recent controversy regarding the meaning and usefulness of weak values is reviewed. It is argued that in spite of recent statistical arguments by Ferrie and Combes, experiments with anomalous weak values provide useful amplification techniques for precision measurements of small effects in many realistic situations. The statistical nature of weak values is questioned. Although measuring weak values requires an ensemble, it is argued that the weak value, similarly to an eigenvalue, is a property of a single pre- and post-selected quantum system.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
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Affiliation(s)
- L Vaidman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel
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6
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Cohen E. What Weak Measurements and Weak Values Really Mean: Reply to Kastner. FOUNDATIONS OF PHYSICS 2017; 47:1261-1266. [PMID: 32009666 PMCID: PMC6961487 DOI: 10.1007/s10701-017-0107-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Accepted: 06/09/2017] [Indexed: 06/10/2023]
Abstract
Despite their important applications in metrology and in spite of numerous experimental demonstrations, weak measurements are still confusing for part of the community. This sometimes leads to unjustified criticism. Recent papers have experimentally clarified the meaning and practical significance of weak measurements, yet in Kastner (Found Phys 47:697-707, 2017), Kastner seems to take us many years backwards in the the debate, casting doubt on the very term "weak value" and the meaning of weak measurements. Kastner appears to ignore both the basics and frontiers of weak measurements and misinterprets the weak measurement process and its outcomes. In addition, she accuses the authors of Aharonov et al. (Ann Phys 355:258-268, 2015) in statements completely opposite to the ones they have actually made. There are many points of disagreement between Kastner and us, but in this short reply I will leave aside the ontology (which is indeed interpretational and far more complex than that described by Kastner) and focus mainly on the injustice in her criticism. I shall add some general comments regarding the broader theory of weak measurements and the two-state-vector formalism, as well as supporting experimental results. Finally, I will point out some recent promising results, which can be proven by (strong) projective measurements, without the need of employing weak measurements.
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Affiliation(s)
- Eliahu Cohen
- H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL UK
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7
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Aharonov Y, Cohen E, Landau A, Elitzur AC. The Case of the Disappearing (and Re-Appearing) Particle. Sci Rep 2017; 7:531. [PMID: 28373649 PMCID: PMC5427996 DOI: 10.1038/s41598-017-00274-w] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2016] [Accepted: 02/15/2017] [Indexed: 11/09/2022] Open
Abstract
A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a particle superposed over three boxes. Under appropriate pre- and post-selections, and with tunneling enabled between two of the boxes, it is possible to derive not only one, but three predictions for three different times within the intermediate interval. These predictions are moreover contradictory. The particle (when looked for using a projective measurement) seems to disappear from the first box where it would have been previously found with certainty, appearing instead within the third box, to which no tunneling is possible, and later re-appearing within the second. It turns out that local measurement (i.e. opening one of the boxes) fails to indicate the particle's presence, but subtler measurements performed on the two boxes together reveal the particle's nonlocal modular momentum spatially separated from its mass. Another advance of this setting is that, unlike other predictions of the TSVF that rely on weak and/or counterfactual measurements, the present one uses actual projective measurements. This outcome is then corroborated by adding weak measurements and the Aharonov-Bohm effect. The results strengthen the recently suggested time-symmetric Heisenberg ontology based on nonlocal deterministic operators. They can be also tested using the newly developed quantum router.
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Affiliation(s)
- Yakir Aharonov
- School of Physics and Astronomy, Tel Aviv University, Tel-Aviv, 6997801, Israel.,Schmid College of Science, Chapman University, Orange, CA, 92866, USA.,Iyar, The Israeli Institute for Advanced Research, POB 651, Zichron, Ya'akov, 3095303, Israel
| | - Eliahu Cohen
- Iyar, The Israeli Institute for Advanced Research, POB 651, Zichron, Ya'akov, 3095303, Israel. .,H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK.
| | - Ariel Landau
- School of Physics and Astronomy, Tel Aviv University, Tel-Aviv, 6997801, Israel
| | - Avshalom C Elitzur
- Iyar, The Israeli Institute for Advanced Research, POB 651, Zichron, Ya'akov, 3095303, Israel
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8
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Piacentini F, Avella A, Levi MP, Gramegna M, Brida G, Degiovanni IP, Cohen E, Lussana R, Villa F, Tosi A, Zappa F, Genovese M. Measuring Incompatible Observables by Exploiting Sequential Weak Values. PHYSICAL REVIEW LETTERS 2016; 117:170402. [PMID: 27824450 DOI: 10.1103/physrevlett.117.170402] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Indexed: 06/06/2023]
Abstract
One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.
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Affiliation(s)
- F Piacentini
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - A Avella
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - M P Levi
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - M Gramegna
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - G Brida
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | | | - E Cohen
- Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - R Lussana
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - F Villa
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - A Tosi
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - F Zappa
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - M Genovese
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy and INFN, Via P. Giuria 1, I-10125 Torino, Italy
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Thekkadath GS, Giner L, Chalich Y, Horton MJ, Banker J, Lundeen JS. Direct Measurement of the Density Matrix of a Quantum System. PHYSICAL REVIEW LETTERS 2016; 117:120401. [PMID: 27689255 DOI: 10.1103/physrevlett.117.120401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2016] [Indexed: 06/06/2023]
Abstract
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
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Affiliation(s)
- G S Thekkadath
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - L Giner
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - Y Chalich
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - M J Horton
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - J Banker
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - J S Lundeen
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
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