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Universality of local weak interactions and its application for interferometric alignment. Proc Natl Acad Sci U S A 2019; 116:2881-2890. [PMID: 30723153 PMCID: PMC6386691 DOI: 10.1073/pnas.1812970116] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The modification of the effect of interactions of a particle as a function of its preselected and postselected states is analyzed theoretically and experimentally. The universality property of this modification in the case of local interactions of a spatially preselected and postselected particle has been found. It allowed us to define an operational approach for the characterization of the presence of a quantum particle in a particular place: the way it modifies the effect of local interactions. The experiment demonstrating this universality property provides an efficient interferometric alignment method, in which the position of the beam on a single detector throughout one phase scan yields all misalignment parameters.
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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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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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Marian D, Zanghì N, Oriols X. Weak Values from Displacement Currents in Multiterminal Electron Devices. PHYSICAL REVIEW LETTERS 2016; 116:110404. [PMID: 27035291 DOI: 10.1103/physrevlett.116.110404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2015] [Indexed: 06/05/2023]
Abstract
Weak values allow the measurement of observables associated with noncommuting operators. Up to now, position-momentum weak values have been mainly developed for (relativistic) photons. In this Letter, a proposal for the measurement of such weak values in typical electronic devices is presented. Inspired by the Ramo-Shockley-Pellegrini theorem that provides a relation between current and electron velocity, it is shown that the displacement current measured in multiterminal configurations can provide either a weak measurement of the momentum or strong measurement of position. This proposal opens new opportunities for fundamental and applied physics with state-of-the-art electronic technology. As an example, a setup for the measurement of the Bohmian velocity of (nonrelativistic) electrons is presented and tested with numerical experiments.
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Affiliation(s)
- D Marian
- Dipartimento di Fisica dell'Università di Genova and INFN sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
- Departament d'Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193-Bellaterra (Barcelona), Spain
| | - N Zanghì
- Dipartimento di Fisica dell'Università di Genova and INFN sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
| | - X Oriols
- Departament d'Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193-Bellaterra (Barcelona), Spain
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Pang S, Brun TA. Improving the Precision of Weak Measurements by Postselection Measurement. PHYSICAL REVIEW LETTERS 2015; 115:120401. [PMID: 26430972 DOI: 10.1103/physrevlett.115.120401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2014] [Indexed: 06/05/2023]
Abstract
Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising result that squeezed coherent states of the pointer can give postselected weak measurements a higher signal-to-noise ratio than standard ones while all standard coherent states cannot, which suggests that raising the precision of weak measurements by postselection calls for the presence of "nonclassicality" in the pointer states. For the second strategy, we show that the quantum Fisher information of postselected weak measurements is generally larger than that of standard weak measurements, even without using the failed postselection events, but the gap can be closed with a proper choice of system state.
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Affiliation(s)
- Shengshi Pang
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
| | - Todd A Brun
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
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Zhang L, Datta A, Walmsley IA. Precision metrology using weak measurements. PHYSICAL REVIEW LETTERS 2015; 114:210801. [PMID: 26066422 DOI: 10.1103/physrevlett.114.210801] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2013] [Indexed: 06/04/2023]
Abstract
Weak values and measurements have been proposed as a means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur with highly suppressed probabilities. This raises three vital questions in weak-measurement-based metrology. Namely, (Q1) Does postselection enhance the measurement precision? (Q2) Does weak measurement offer better precision than strong measurement? (Q3) Is it possible to beat the standard quantum limit or to achieve the Heisenberg limit with weak measurement using only classical resources? We analyze these questions for two prototypical, and generic, measurement protocols and show that while the answers to the first two questions are negative for both protocols, the answer to the last is affirmative for measurements with phase-space interactions, and negative for configuration space interactions. Our results, particularly the ability of weak measurements to perform at par with strong measurements in some cases, are instructive for the design of weak-measurement-based protocols for quantum metrology.
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Affiliation(s)
- Lijian Zhang
- National Laboratory of Solid State Microstructures and College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Max Planck Institute for Structure and Dynamics of Material, Hamburg 22761, Germany
| | - Animesh Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
- Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Ian A Walmsley
- Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
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Gendra B, Calsamiglia J, Muñoz-Tapia R, Bagan E, Chiribella G. Probabilistic metrology attains macroscopic cloning of quantum clocks. PHYSICAL REVIEW LETTERS 2014; 113:260402. [PMID: 25615289 DOI: 10.1103/physrevlett.113.260402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2014] [Indexed: 06/04/2023]
Abstract
It has recently been shown that probabilistic protocols based on postselection boost the performances of the replication of quantum clocks and phase estimation. Here we demonstrate that the improvements in these two tasks have to match exactly in the macroscopic limit where the number of clones grows to infinity, preserving the equivalence between asymptotic cloning and state estimation for arbitrary values of the success probability. Remarkably, the cloning fidelity depends critically on the number of rationally independent eigenvalues of the clock Hamiltonian. We also prove that probabilistic metrology can simulate cloning in the macroscopic limit for arbitrary sets of states when the performance of the simulation is measured by testing small groups of clones.
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Affiliation(s)
- B Gendra
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - J Calsamiglia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - R Muñoz-Tapia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - E Bagan
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - G Chiribella
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
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Pang S, Dressel J, Brun TA. Entanglement-assisted weak value amplification. PHYSICAL REVIEW LETTERS 2014; 113:030401. [PMID: 25083620 DOI: 10.1103/physrevlett.113.030401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2014] [Indexed: 06/03/2023]
Abstract
Large weak values have been used to amplify the sensitivity of a linear response signal for detecting changes in a small parameter, which has also enabled a simple method for precise parameter estimation. However, producing a large weak value requires a low postselection probability for an ancilla degree of freedom, which limits the utility of the technique. We propose an improvement to this method that uses entanglement to increase the efficiency. We show that by entangling and postselecting n ancillas, the postselection probability can be increased by a factor of n while keeping the weak value fixed (compared to n uncorrelated attempts with one ancilla), which is the optimal scaling with n that is expected from quantum metrology. Furthermore, we show the surprising result that the quantum Fisher information about the detected parameter can be almost entirely preserved in the postselected state, which allows the sensitive estimation to approximately saturate the relevant quantum Cramér-Rao bound. To illustrate this protocol we provide simple quantum circuits that can be implemented using current experimental realizations of three entangled qubits.
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Affiliation(s)
- Shengshi Pang
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
| | - Justin Dressel
- Department of Electrical Engineering, University of California, Riverside, California 92521, USA
| | - Todd A Brun
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
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Shomroni I, Bechler O, Rosenblum S, Dayan B. Demonstration of weak measurement based on atomic spontaneous emission. PHYSICAL REVIEW LETTERS 2013; 111:023604. [PMID: 23889401 DOI: 10.1103/physrevlett.111.023604] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2012] [Indexed: 06/02/2023]
Abstract
We demonstrate a new type of weak measurement based on the dynamics of spontaneous emission. The pointer in our scheme is given by the Lorentzian distribution characterizing atomic exponential decay via emission of a single photon. We thus introduce weak measurement, so far demonstrated nearly exclusively with laser beams and Gaussian statistics, into the quantum regime of single emitters and single quanta, enabling the exploitation of a wide class of sources that are abundant in nature. We describe a complete analogy between our scheme and weak measurement with conventional Gaussian pointers. Instead of a shift in the mean of a Gaussian distribution, an imaginary weak value is exhibited in our scheme by a significantly slower-than-natural exponential distribution of emitted photons at the postselected polarization, leading to a large shift in their mean arrival time. The dynamics of spontaneous emission offer a broader view of the measurement process than is usually considered within the weak measurement formalism. Our scheme opens the path for the use of atoms and atomlike systems as sensitive probes in weak measurements, one example being optical magnetometry.
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Affiliation(s)
- Itay Shomroni
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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Zilberberg O, Romito A, Starling DJ, Howland GA, Broadbent CJ, Howell JC, Gefen Y. Null values and quantum state discrìmination. PHYSICAL REVIEW LETTERS 2013; 110:170405. [PMID: 23679690 DOI: 10.1103/physrevlett.110.170405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2012] [Revised: 02/19/2013] [Indexed: 06/02/2023]
Abstract
We present a measurement protocol for discriminating between two different quantum states of a qubit with high fidelity. The protocol, called null value, is comprised of a projective measurement performed on the system with a small probability (also known as partial collapse), followed by a tuned postselection. We report on an optical experimental implementation of the scheme. We show that our protocol leads to an amplified signal-to-noise ratio (as compared with a straightforward strong measurement) when discerning between the two quantum states.
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Affiliation(s)
- Oded Zilberberg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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11
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Strübi G, Bruder C. Measuring ultrasmall time delays of light by joint weak measurements. PHYSICAL REVIEW LETTERS 2013; 110:083605. [PMID: 23473146 DOI: 10.1103/physrevlett.110.083605] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2012] [Indexed: 06/01/2023]
Abstract
We propose to use weak measurements away from the weak-value amplification regime to carry out precision measurements of time delays of light. Our scheme is robust to several sources of noise that are shown to only limit the relative precision of the measurement. Thus, they do not set a limit on the smallest measurable phase shift, contrary to standard interferometry and weak-value-based measurement techniques. Our idea is not restricted to phase-shift measurements and could be used to measure other small effects using a similar protocol.
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Affiliation(s)
- Grégory Strübi
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
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12
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Abstract
Recent work has revealed that the wave function of a pure state can be measured directly and that complementary knowledge of a quantum system can be obtained simultaneously by weak measurements. However, the original scheme applies only to pure states, and it is not efficient because most of the data are discarded by post-selection. Here, we propose tomography schemes for pure states and for mixed states via weak measurements, and our schemes are more efficient because we do not discard any data. Furthermore, we demonstrate that any matrix element of a general state can be directly read from an appropriate weak measurement. The density matrix (with all of its elements) represents all that is directly accessible from a general measurement.
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Affiliation(s)
- Shengjun Wu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
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Wu S, Zukowski M. Feasible optical weak measurements of complementary observables via a single Hamiltonian. PHYSICAL REVIEW LETTERS 2012; 108:080403. [PMID: 22463503 DOI: 10.1103/physrevlett.108.080403] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2011] [Revised: 11/21/2011] [Indexed: 05/31/2023]
Abstract
A general formalism for joint weak measurements of a pair of complementary observables is given. The standard process of optical three-wave mixing in a nonlinear crystal (such as in parametric down-conversion) is suitable for such tasks. To obtain the weak value of a variable A one performs weak measurements twice, with different initial states of the meter field. This seems to be a drawback, but as a compensation we get for free the weak value of a complementary variable B. The scheme is tunable and versatile: one has access to a continuous set of possible weak measurements of a pair of observables. The scheme increases signal-to-noise ratio with respect to the case without postselection.
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Affiliation(s)
- Shengjun Wu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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