Investigating the Effects of the Interaction Intensity in a Weak Measurement

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.

[1]  Lev Vaidman,et al.  The meaning of protective measurements , 1994 .

[2]  L Vaidman,et al.  Weak value controversy , 2017, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[3]  Zach DeVito,et al.  Opt , 2017 .

[4]  J. Lundeen,et al.  Direct measurement of the quantum wavefunction , 2011, Nature.

[5]  Benni Reznik,et al.  Revisiting Hardy's Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values , 2001 .

[6]  A. K. Pan,et al.  Joint weak value for all order coupling using continuous variable and qubit probe , 2017, 1708.07327.

[7]  Yutaka Shikano,et al.  Weak values with decoherence , 2008, 0812.4502.

[8]  M P Almeida,et al.  Violation of the Leggett–Garg inequality with weak measurements of photons , 2009, Proceedings of the National Academy of Sciences.

[9]  Onur Hosten,et al.  Observation of the Spin Hall Effect of Light via Weak Measurements , 2008, Science.

[10]  J. Hou,et al.  Quantum correlation based on weak measurements , 2017 .

[11]  Guang-Can Guo,et al.  Phase estimation with weak measurement using a white light source. , 2013, Physical review letters.

[12]  Marco Barbieri,et al.  Anomalous weak values and the violation of a multiple-measurement Leggett-Garg inequality , 2017 .

[13]  Experimental weak measurement of two non-commuting observables , 2016, 1610.04464.

[14]  Ritchie,et al.  Realization of a measurement of a "weak value" , 1991, Physical review letters.

[15]  Shan Geo.  Protective Measurement and Quantum Reality: Protective measurement: an introduction , 2015 .

[16]  Structural features of sequential weak measurements , 2015, 1511.03923.

[17]  A. Lorenzo.  Full counting statistics of weak-value measurement , 2011, 1109.4183.

[18]  A. Jordan,et al.  Weak values and the Leggett-Garg inequality in solid-state qubits. , 2007, Physical review letters.

[19]  Lev Vaidman,et al.  Weak value beyond conditional expectation value of the pointer readings , 2016, 1611.03989.

[20]  Maximilian Schlosshauer.  Measuring the quantum state of a single system with minimum state disturbance , 2016 .

[21]  Yuki Susa,et al.  Optimal probe wave function of weak-value amplification , 2012, 1203.0827.

[22]  T. Geszti.  Postselected weak measurement beyond the weak value , 2009, 0909.2206.

[23]  Aephraim M. Steinberg,et al.  Weak-value amplification of the nonlinear effect of a single photon , 2017, Nature Physics.

[24]  W. Brockherde,et al.  CMOS Imager With 1024 SPADs and TDCs for Single-Photon Timing and 3-D Time-of-Flight , 2014, IEEE Journal of Selected Topics in Quantum Electronics.

[25]  Shan Gao.  Protective Measurement and Quantum Reality: Towards a New Understanding of Quantum Mechanics , 2014 .

[26]  Franco Nori,et al.  Nonperturbative theory of weak pre-and post-selected measurements , 2011, 1109.6315.

[27]  J. E. Gray,et al.  Variance control in weak-value measurement pointers , 2011 .

[28]  S. Wen,et al.  Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements , 2011, 1112.4560.

[29]  Berthold-Georg Englert,et al.  PROTECTIVE MEASUREMENTS AND BOHM TRAJECTORIES , 1999 .

[30]  A. Pati,et al.  Products of weak values: Uncertainty relations, complementarity, and incompatibility , 2016, 1603.05776.

[31]  Yoon-Ho Kim,et al.  Weak value measurement with an incoherent measuring device , 2009, CLEO/QELS: 2010 Laser Science to Photonic Applications.

[32]  S. Wen,et al.  Observation of Spin Hall Effect in Photon Tunneling via Weak Measurements , 2014, Scientific Reports.

[33]  A. Jordan,et al.  Strengthening weak-value amplification with recycled photons , 2013, 1305.4520.

[34]  A. Aspect,et al.  A New Light on Single Photon Interferences , 1986 .

[35]  Yakir AharonovandLev Vaidman.  Measurement of the Schrodingerwaveof a single particle , 1993 .

[36]  K J Resch.  Amplifying a Tiny Optical Effect , 2008, Science.

[37]  G S Thekkadath,et al.  Direct Measurement of the Density Matrix of a Quantum System. , 2016, Physical review letters.

[38]  J. Howell,et al.  Practical advantages of almost-balanced-weak-value metrological techniques , 2017, 1703.01632.

[39]  Richard Jozsa,et al.  Sequential weak measurement , 2007, 0706.1508.

[40]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[41]  Eliahu Cohen,et al.  Introduction to Weak Measurements and Weak Values , 2013 .

[42]  Jos Uffink.  How to protect the interpretation of the wave function against protective measurements , 1999 .

[43]  David J. Starling,et al.  Continuous phase amplification with a Sagnac interferometer , 2009, 0912.2357.

[44]  A. Jordan,et al.  Weak values are universal in von Neumann measurements. , 2012, Physical review letters.

[45]  H M Wiseman,et al.  Measurement of quantum weak values of photon polarization. , 2005, Physical review letters.

[46]  A. Tosi,et al.  Determining the quantum expectation value by measuring a single photon , 2017, Nature Physics.

[47]  M. Genovese,et al.  Interpretations of Quantum Mechanics and the measurement problem , 2010, 1002.0990.

[48]  J. Howell,et al.  Anomalous amplification of a homodyne signal via almost-balanced weak values. , 2016, Optics letters.

[49]  David J. Starling,et al.  Ultrasensitive beam deflection measurement via interferometric weak value amplification. , 2009, Physical review letters.

[50]  G. Jayaswal,et al.  Observing angular deviations in light-beam reflection via weak measurements. , 2014, Optics letters.

[51]  P. Grangier,et al.  Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences , 1986 .

[52]  Vaidman,et al.  How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. , 1988, Physical review letters.

[53]  Robert W. Boyd,et al.  Full characterization of polarization states of light via direct measurement , 2012, Nature Photonics.

[54]  A. Jordan,et al.  Significance of the imaginary part of the weak value , 2011, 1112.3986.

[55]  A. Jordan,et al.  Contextual values of observables in quantum measurements. , 2009, Physical review letters.

[56]  Marco Genovese,et al.  Improved implementation of the Alicki-Van Ryn nonclassicality test for a single particle using Si detectors , 2009 .

[57]  Yuen,et al.  Impossibility of measuring the wave function of a single quantum system. , 1996, Physical review letters.

[59]  A. Jordan,et al.  Colloquium : Understanding quantum weak values: Basics and applications , 2013, 1305.7154.

[60]  Unruh.  Reality and measurement of the wave function. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[61]  N. D. Hari Dass,et al.  Critique of protective measurements , 1999 .

[62]  J.Samuel,et al.  Comment on ``Meaning of the Wave Function'' , 1994 .

[63]  Amplification of Angular Rotations using Weak Measurements , 2014 .

[64]  Matthew F Pusey.  Anomalous weak values are proofs of contextuality. , 2014, Physical review letters.

[65]  J. Dressel,et al.  Confined contextuality in neutron interferometry: Observing the quantum pigeonhole effect , 2016, 1609.06046.

[66]  L. Vaidman,et al.  Protective Measurements of Two-State Vectors , 1997 .

[67]  Ognyan Oreshkov,et al.  Weak measurements are universal. , 2005, Physical review letters.

[68]  A Tosi,et al.  Measuring Incompatible Observables by Exploiting Sequential Weak Values. , 2016, Physical review letters.

[69]  Eliahu Cohen,et al.  Can a future choice affect a past measurement’s outcome? , 2015 .

[70]  A Tosi,et al.  Experiment Investigating the Connection between Weak Values and Contextuality. , 2016, Physical review letters.

[71]  Guihua Zeng,et al.  Ultra-small time-delay estimation via a weak measurement technique with post-selection , 2015, 1509.04003.

[72]  A. Migdall,et al.  Spatial and spectral mode selection of heralded single photons from pulsed parametric down-conversion. , 2005, Optics express.

[73]  Eliahu Cohen,et al.  Foundations and Applications Of Weak Quantum Measurements , 2014 .

[74]  S. Chiow,et al.  Precision angle sensor using an optical lever inside a Sagnac interferometer. , 2011, Optics letters.

[75]  Howard Mark Wiseman,et al.  Weak values, quantum trajectories, and the cavity-QED experiment on wave-particle correlation , 2002 .

[76]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[77]  John C Howell,et al.  Ultrasensitive inverse weak-value tilt meter. , 2017, Optics letters.