Laser & Optoelectronics Progress, Volume. 58, Issue 10, 1011004(2021)
Progress in Weak-Value-Based Quantum Metrology and Tomography
[1] Aharonov Y, Vaidman L. Properties of a quantum system during the time interval between two measurements[J]. Physical Review A, Atomic, Molecular, and Optical Physics, 41, 11-20(1990).
[2] Aharonov Y, Bergmann P G, Lebowitz J L. Time symmetry in the quantum process of measurement[J]. Physical Review, 134, B1410-B1416(1964).
[3] Xu X Y, Pan W W, Wang Q Q et al. Measurements of nonlocal variables and demonstration of the failure of the product rule for a pre- and postselected pair of photons[J]. Physical Review Letters, 122, 100405(2019).
[4] Aharonov Y, Vaidman L. On the two-state vector reformulation of quantum mechanics[J]. Physica Scripta, T76, 85(1998).
[5] Aharonov Y, Vaidman L. The two-state vector formalism: an updated review[M]. //Muga J G, Mayato R S, Egusquiza Í L. Time in quantum mechanics. Lecture notes in physics. Heidelberg: Springer, 734, 399-477(2008).
[6] Aharonov Y, Popescu S, Tollaksen J. A time-symmetric formulation of quantum mechanics[J]. Physics Today, 63, 27-32(2010).
[7] Aharonov Y, Albert D Z, Vaidman L. How the result of a measurement of a component of the spin of a spin- 1/2 particle can turn out to be 100[J]. Physical Review Letters, 60, 1351-1354(1988).
[8] Kofman A G, Ashhab S, Nori F. Nonperturbative theory of weak pre- and post-selected measurements[J]. Physics Reports, 520, 43-133(2012).
[9] Dressel J, Jordan A N. Weak-values are universal in von Neumann measurements[J]. Physical Review Letters, 109, 230402(2012).
[10] Tamir B, Cohen E. Introduction to weak measurements and weak-values[J]. Quanta, 2, 7-17(2013).
[11] Dressel J, Malik M, Miatto F M et al. Colloquium: understanding quantum weak-values: basics and applications[J]. Reviews of Modern Physics, 86, 307-316(2014).
[12] Knee G C, Combes J, Ferrie C et al. Weak-value amplification: state of play[J]. Quantum Measurements and Quantum Metrology, 3, 32-37(2016).
[13] Steinberg A M. A light touch[J]. Nature, 463, 890-891(2010).
[14] Aharonov Y, Botero A. Quantum averages of weak-values[J]. Physical Review A, 72, 052111(2005).
[17] Lundeen J S, Steinberg A M. Experimental joint weak measurement on a photon pair as a probe of Hardy’s paradox[J]. Physical Review Letters, 102, 020404(2009).
[18] Resch K J, Lundeen J S, Steinberg A M. Experimental realization of the quantum box problem[J]. Physics Letters A, 324, 125-131(2004).
[20] Dressel J, Broadbent C J, Howell J C et al. Experimental violation of two-party Leggett-Garg inequalities with semiweak measurements[J]. Physical Review Letters, 106, 040402(2011).
[25] Dressel J, Jordan A N. Significance of the imaginary part of the weak-value[J]. Physical Review A, 85, 012107(2012).
[26] Brunner N, Acín A, Collins D et al. Optical telecom networks as weak quantum measurements with postselection[J]. Physical Review Letters, 91, 180402(2003).
[27] Brunner N, Scarani V, Wegmüller M et al. Direct measurement of superluminal group velocity and signal velocity in an optical fiber[J]. Physical Review Letters, 93, 203902(2004).
[28] Solli D R, McCormick C F, Chiao R Y et al. Fast light, slow light, and phase singularities: a connection to generalized weak-values[J]. Physical Review Letters, 92, 043601(2004).
[29] Camacho R M, Dixon P B, Glasser R T et al. Realization of anall-optical zero to pi cross-phase modulation jump[J]. Physical Review Letters, 102, 013902(2009).
[30] Cho Y W, Kim Y, Choi Y H et al. Emergence of the geometric phase from quantum measurement back-action[J]. Nature Physics, 15, 665-670(2019).
[32] von Neumann J. Mathematical foundations of quantum mechanics: new edition[M](2018).
[34] Parks A D, Gray J E. Variance control in weak-value measurement pointers[J]. Physical Review A, 84, 012116(2011).
[38] Pryde G J, O’Brien J L, White A G et al. Measurement of quantum weak-values of photon polarization[J]. Physical Review Letters, 94, 220405(2005).
[39] Romito A, Gefen Y, Blanter Y M. Weak-values of electron spin in a double quantum dot[J]. Physical Review Letters, 100, 056801(2008).
[40] Shpitalnik V, Gefen Y, Romito A. Tomography of many-body weak-values: Mach-Zehnder interferometry[J]. Physical Review Letters, 101, 226802(2008).
[41] Cho Y W, Lim H T, Ra Y S et al. Weak-value measurement with an incoherent measuring device[C]. //CLEO/QELS: 2010 Laser Science to Photonic Applications, May 16-21, 2010, San Jose, CA, USA, 1-2(2010).
[42] Shikano Y, Hosoya A. Weak-values with decoherence[J]. Journal of Physics A, 43, 025304(2010).
[43] Iinuma M, Suzuki Y, Taguchi G et al. Weak measurement of photon polarization by back-action-induced path interference[J]. New Journal of Physics, 13, 033041(2011).
[46] Susa Y, Shikano Y, Hosoya A. Optimal probe wave function of weak-value amplification[J]. Physical Review A, 85, 052110(2012).
[47] Turek Y, Kobayashi H, Akutsu T et al. Post-selected von Neumann measurement with Hermite-Gaussian and Laguerre-Gaussian pointer states[J]. New Journal of Physics, 17, 083029(2015).
[49] Qin L P, Feng W, Li X Q. Simple understanding of quantum weak-values[J]. Scientific Reports, 6, 20286(2016).
[51] Ogawa K, Kobayashi H, Tomita A. Operational formulation of weak-values without probe systems[J]. Physical Review A, 101, 042117(2020).
[52] Wu S J, Li Y. Weak measurements beyond the Aharonov-Albert-Vaidman formalism[J]. Physical Review A, 83, 052106(2011).
[55] Zhu X M, Zhang Y X, Pang S S et al. Quantum measurements with preselection and postselection[J]. Physical Review A, 84, 052111(2011).
[56] di Lorenzo A. Full counting statistics of weak-value measurement[J]. Physical Review A, 85, 032106(2012).
[57] Nakamura K, Nishizawa A, Fujimoto M K. Evaluation of weak measurements to all orders[J]. Physical Review A, 85, 012113(2012).
[58] Nishizawa A, Nakamura K, Fujimoto M K. Weak-value amplification in a shot-noise-limited interferometer[J]. Physical Review A, 85, 062108(2012).
[59] Chen S Z, Zhou X X, Mi C Q et al. Modified weak measurements for the detection of the photonic spin Hall effect[J]. Physical Review A, 91, 062105(2015).
[60] Qiu J D, Ren C L, Li Z X et al. Extended validity of weak measurement[J]. Chinese Physics B, 29, 064214(2020).
[62] Pang S S, Wu S J, Chen Z B. Weak measurement with orthogonal preselection and postselection[J]. Physical Review A, 86, 022112(2012).
[63] Ritchie N W M, Story J G, Hulet R G. Realization of a measurement of a“weak-value”[J]. Physical Review Letters, 66, 1107-1110(1991).
[64] Hosten O, Kwiat P. Observation of the spin Hall effect of light via weak measurements[J]. Science, 319, 787-790(2008).
[66] Howell J C, Starling D J, Dixon P B et al. Interferometric weak-value deflections: quantum and classical treatments[J]. Physical Review A, 81, 033813(2010).
[69] Starling D J, Dixon P B, Williams N S et al. Continuous phase amplification with a Sagnac interferometer[J]. Physical Review A, 82, 011802(2010).
[70] Starling D J, Dixon P B, Jordan A N et al. Precision frequency measurements with interferometric weak-values[J]. Physical Review A, 82, 063822(2010).
[72] Zilberberg O, Romito A, Gefen Y. Charge sensing amplification via weak-values measurement[J]. Physical Review Letters, 106, 080405(2011).
[74] Hogan J M, Hammer J, Chiow S W et al. Precision angle sensor using an optical lever inside a Sagnac interferometer[J]. Optics Letters, 36, 1698-1700(2011).
[75] Pfeifer M, Fischer P. Weak-value amplified optical activity measurements[J]. Optics Express, 19, 16508-16517(2011).
[78] Egan P, Stone J A. Weak-value thermostat with 0.2 mK precision[J]. Optics Letters, 37, 4991-4993(2012).
[81] Li C F, Xu X Y, Tang J S et al. Ultrasensitive phase estimation with white light[J]. Physical Review A, 83, 044102(2011).
[84] Magaña-Loaiza O S, Mirhosseini M, Rodenburg B et al. Amplification of angular rotations using weak measurements[C]. //Frontiers in Optics 2014, October 19-23, 2014, Tucson, Arizona United States. Washington, D.C.: OSA, FTh4A.4(2014).
[85] Hallaji M, Feizpour A, Dmochowski G et al. Weak-value amplification of the nonlinear effect of a single photon[J]. Nature Physics, 13, 540-544(2017).
[88] Chen S Z, Mi C Q, Wu W J et al. Weak-value amplification for Weyl-point separation in momentum space[J]. New Journal of Physics, 20, 103050(2018).
[91] Giovannetti V, Lloyd S, Maccone L. Advances in quantum metrology[J]. Nature Photonics, 5, 222-229(2011).
[92] Braunstein S L. Quantum limits on precision measurements of phase[J]. Physical Review Letters, 69, 3598-3601(1992).
[94] Giovannetti V, Lloyd S, Maccone L. Quantum metrology[J]. Physical Review Letters, 96, 010401(2006).
[95] Resch K J, Pregnell K L, Prevedel R et al. Time-reversal and super-resolving phase measurements[J]. Physical Review Letters, 98, 223601(2007).
[96] Polino E, Valeri M, Spagnolo N et al. Photonic quantum metrology[J]. AVS Quantum Science, 2, 024703(2020).
[99] Lee J, Tsutsui I. Merit of amplification by weak measurement in view of measurement uncertainty[J]. Quantum Studies: Mathematics and Foundations, 1, 65-78(2014).
[100] Combes J, Ferrie C. Cost of postselection in decision theory[J]. Physical Review A, 92, 022117(2015).
[101] Susa Y, Tanaka S. Statistical hypothesis testing by weak-value amplification: proposal and evaluation[J]. Physical Review A, 92, 012112(2015).
[103] Zhang L J, Datta A, Walmsley I A. Precision metrology using weak measurements[J]. Physical Review Letters, 114, 210801(2015).
[104] Hofmann H F, Goggin M E, Almeida M P et al. Estimation of a quantum interaction parameter using weak measurements: theory and experiment[J]. Physical Review A, 86, 040102(2012).
[106] Alves G B, Escher B M, de Matos Filho R L et al. Weak-value amplification as an optimal metrological protocol[J]. Physical Review A, 91, 062107(2015).
[108] Xu L, Liu Z X, Datta A et al. Approaching quantum-limited metrology with imperfect detectors by using weak-value amplification[J]. Physical Review Letters, 125, 080501(2020).
[109] Pang S S, Dressel J, Brun T A. Entanglement-assisted weak-value amplification[J]. Physical Review Letters, 113, 030401(2014).
[111] Stárek R, Mičuda M, Hošák R et al. Experimental entanglement-assisted weak measurement of phase shift[J]. Optics Express, 28, 34639-34655(2020).
[112] Pang S S, Brun T A. Suppressing technical noise in weak measurements by entanglement[J]. Physical Review A, 92, 012120(2015).
[114] Jordan A N, Tollaksen J, Troupe J E et al. Heisenberg scaling with weak measurement:a quantum state discrimination point of view[J]. Quantum Studies: Mathematics and Foundations, 2, 5-15(2015).
[115] Chen G, Zhang L J, Zhang W H et al. Achieving Heisenberg-scaling precision with projective measurement on single photons[J]. Physical Review Letters, 121, 060506(2018).
[116] Chen G, Aharon N, Sun Y N et al. Heisenberg-scaling measurement of the single-photon Kerr non-linearity using mixed states[J]. Nature Communications, 9, 93(2018).
[117] Torres J P, Salazar-Serrano L J. Weak-value amplification: a view from quantum estimation theory that highlights what it is and what isn’t[J]. Scientific Reports, 6, 19702(2016).
[118] Knee G C, Briggs G A D, Benjamin S C et al. Quantum sensors based on weak-value amplification cannot overcome decoherence[J]. Physical Review A, 87, 012115(2013).
[119] Pang S S, Alonso J R G, Brun T A et al. Protecting weak measurements against systematic errors[J]. Physical Review A, 94, 012329(2016).
[121] Jordan A N, Martínez-Rincón J, Howell J C. Technical advantages for weak-value amplification: when less is more[J]. Physical Review X, 4, 011031(2014).
[122] Sinclair J, Hallaji M, Steinberg A M et al. Weak-value amplification and optimal parameter estimation in the presence of correlated noise[J]. Physical Review A, 96, 052128(2017).
[123] Starling D J, Dixon P B, Jordan A N et al. Optimizing the signal-to-noise ratio of a beam-deflection measurement with interferometric weak-values[J]. Physical Review A, 80, 041803(2009).
[125] Knee G C, Gauger E M. When amplification with weak-values fails to suppress technical noise[J]. Physical Review X, 4, 011032(2014).
[126] Viza G I, Martínez-Rincón J, Alves G B et al. Experimentally quantifying the advantages of weak-values-based metrology[C]. //CLEO: QELS_Fundamental Science 2015, May 10-15, 2015, San Jose, California United States. Washington, D.C.: OSA, FM1A.2(2015).
[127] Harris J, Boyd R W, Lundeen J S. Weak-value amplification can outperform conventional measurement in the presence of detector saturation[J]. Physical Review Letters, 118, 070802(2017).
[129] Lyons K, Dressel J, Jordan A N et al. Power-recycled weak-value-based metrology[J]. Physical Review Letters, 114, 170801(2015).
[130] Wang Y T, Tang J S, Hu G et al. Experimental demonstration of higher precision weak-value-based metrology using power recycling[J]. Physical Review Letters, 117, 230801(2016).
[131] Strübi G, Bruder C. Measuring ultrasmall time delays of light by joint weak measurements[J]. Physical Review Letters, 110, 083605(2013).
[132] Fang C, Huang J Z, Yu Y et al. Ultra-small time-delay estimation via a weak measurement technique with post-selection[J]. Journal of Physics B, 49, 175501(2016).
[133] Martínez-Rincón J, Liu W T, Viza G I et al. Can anomalous amplification be attained without postselection?[J]. Physical Review Letters, 116, 100803(2016).
[135] Martínez-Rincón J, Mullarkey C A, Viza G I et al. Ultrasensitive inverse weak-value tilt meter[J]. Optics Letters, 42, 2479-2482(2017).
[136] Lyons K, Howell J C, Jordan A N. Noise suppression in inverse weak-value-based phase detection[J]. Quantum Studies: Mathematics and Foundations, 5, 579-588(2018).
[138] Zhang Z H, Chen G, Xu X Y et al. Ultrasensitive biased weak measurement for longitudinal phase estimation[J]. Physical Review A, 94, 053843(2016).
[139] Li D M, Guan T, He Y H et al. A chiral sensor based on weak measurement for the determination of Proline enantiomers in diverse measuring circumstances[J]. Biosensors and Bioelectronics, 110, 103-109(2018).
[141] Thew R T, Nemoto K, White A G et al. Qudit quantum-state tomography[J]. Physical Review A, 66, 012303(2002).
[142] James D F V, Kwiat P G, Munro W J et al. Measurement of qubits[J]. Physical Review A, 64, 052312(2001).
[143] Horodecki R, Horodecki P, Horodecki M et al. Quantum entanglement[J]. Reviews of Modern Physics, 81, 865-942(2009).
[145] Pallister S, Linden N, Montanaro A. Optimal verification of entangled states with local measurements[J]. Physical Review Letters, 120, 170502(2018).
[147] Fischbach J, Freyberger M. Quantum optical reconstruction scheme using weak values[J]. Physical Review A, 86, 052110(2012).
[149] Malik M, Mirhosseini M, Lavery M P J et al. Direct measurement of a 27-dimensional orbital-angular-momentum state vector[J]. Nature Communications, 5, 3115(2014).
[153] Mao Y L, Ma Z H, Jin R B et al. Error-disturbance trade-off in sequential quantum measurements[J]. Physical Review Letters, 122, 090404(2019).
[155] di Lorenzo A. Sequential measurement of conjugate variables as an alternative quantum state tomography[J]. Physical Review Letters, 110, 010404(2013).
[156] Diósi L. Structural features of sequential weak measurements[J]. Physical Review A, 94, 010103(2016).
[158] Chen J S, Hu M J, Hu X M et al. Experimental realization of sequential weak measurements of non-commuting Pauli observables[J]. Optics Express, 27, 6089-6097(2019).
[163] Brodutch A, Vaidman L. Measurements of non local weak-values[J]. Journal of Physics: Conference Series, 174, 012004(2009).
[166] Kim Y, Kim Y S, Lee S Y et al. Direct quantum process tomography via measuring sequential weak-values of incompatible observables[J]. Nature Communications, 9, 192(2018).
[170] Zhang L J, Datta A, Coldenstrodt-Ronge H B et al. Recursive quantum detector tomography[J]. New Journal of Physics, 14, 115005(2012).
[171] Lundeen J S, Feito A, Coldenstrodt-Ronge H et al. Tomography of quantum detectors[J]. Nature Physics, 5, 27-30(2009).
[172] Barnett S M, Pegg D T, Jeffers J. Bayes’ theorem and quantum retrodiction[J]. Journal of Modern Optics, 47, 1779-1789(2000).
[177] Maccone L, Rusconi C C. State estimation: a comparison between direct state measurement and tomography[J]. Physical Review A, 89, 022122(2014).
[179] Vallone G, Dequal D. Strong measurements give a better direct measurement of the quantum wave function[J]. Physical Review Letters, 116, 040502(2016).
[180] Zhang Y X, Wu S J, Chen Z B. Coupling-deformed pointer observables and weak-values[J]. Physical Review A, 93, 032128(2016).
[181] Zhu X M, Zhang Y X, Wu S J. Direct state reconstruction with coupling-deformed pointer observables[J]. Physical Review A, 93, 062304(2016).
[182] Denkmayr T, Geppert H, Lemmel H et al. Experimental demonstration of direct path state characterization by strongly measuring weak-values in a matter-wave interferometer[J]. Physical Review Letters, 118, 010402(2017).
[185] Zhang C R, Hu M J, Hou Z B et al. Direct measurement of the two-dimensional spatial quantum wave function via strong measurements[J]. Physical Review A, 101, 012119(2020).
[186] Howland G A, Lum D J, Howell J C. Compressive wavefront sensing with weak-values[J]. Optics Express, 22, 18870-18880(2014).
[187] Mirhosseini M, Magaña-Loaiza O S, Hashemi Rafsanjani S M et al. Compressive direct measurement of the quantum wave function[J]. Physical Review Letters, 113, 090402(2014).
[188] Knarr S H, Lum D J, Schneeloch J et al. Compressive direct imaging of a billion-dimensional optical phase space[J]. Physical Review A, 98, 023854(2018).
[189] Shi Z M, Mirhosseini M, Margiewicz J et al. Scan-free direct measurement of an extremely high-dimensional photonic state[J]. Optica, 2, 388-392(2015).
[190] Ogawa K, Yasuhiko O, Kobayashi H et al. A framework for measuring weak-values without weak interactions and its diagrammatic representation[J]. New Journal of Physics, 21, 043013(2019).
[193] Yang M, Xiao Y, Liao Y W et al. Zonal reconstruction of photonic wavefunction via momentum weak measurement[J]. Laser & Photonics Reviews, 14, 1900251(2020).
Get Citation
Copy Citation Text
Liang Xu, Lijian Zhang. Progress in Weak-Value-Based Quantum Metrology and Tomography[J]. Laser & Optoelectronics Progress, 2021, 58(10): 1011004
Category: Imaging Systems
Received: Apr. 8, 2021
Accepted: Apr. 23, 2021
Published Online: May. 28, 2021
The Author Email: Zhang Lijian (lijian.zhang@nju.edu.cn)