What Weak Measurements and Weak Values Really Mean: Reply to Kastner

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.

[1]  J. Linnett,et al.  Quantum mechanics , 1975, Nature.

[2]  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.

[3]  L. Hardy,et al.  Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. , 1992, Physical review letters.

[4]  Aharonov,et al.  Quantum random walks. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[5]  Michael V Berry,et al.  Evanescent and real waves in quantum billiards and Gaussian beams , 1994 .

[6]  J. Anandan,et al.  Quantum Coherenece and Reality, In Celebration of the 60th Birthday of Yakir Aharonov , 1995 .

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

[8]  Y. Aharonov,et al.  Two-time interpretation of quantum mechanics , 2005, quant-ph/0507269.

[9]  Yakir Aharonov,et al.  Quantum Paradoxes: Quantum Theory for the Perplexed , 2005 .

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

[11]  O. Zilberberg,et al.  Charge sensing amplification via weak values measurement. , 2010, Physical review letters.

[12]  Aephraim M. Steinberg,et al.  Amplifying single-photon nonlinearity using weak measurements. , 2010, Physical review letters.

[13]  Aephraim M. Steinberg,et al.  Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer , 2011, Science.

[14]  John C. Howell,et al.  Technical advantages for weak value amplification: When less is more , 2013, 1309.5011.

[15]  L Vaidman,et al.  Asking photons where they have been. , 2013, Physical review letters.

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

[17]  Unusual Interactions of Pre-and-Post-Selected Particles , 2014 .

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

[19]  E. Cohen.  A comment on "How the result of a single coin toss can turn out to be 100 heads" , 2014, 1409.8555.

[20]  Y. Aharonov,et al.  Measurement and collapse within the two-state vector formalism , 2014, 1406.6382.

[21]  John C. Howell,et al.  Experimentally quantifying the advantages of weak-values-based metrology , 2014, 2015 Conference on Lasers and Electro-Optics (CLEO).

[22]  Y. Aharonov,et al.  A nonlocal ontology underlying the time-symmetric Heisenberg representation , 2015, 1510.03084.

[23]  Experimentally quantifying the advantages of weak-values-based metrology , 2015, 2015 Conference on Lasers and Electro-Optics (CLEO).

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

[25]  S. Takeuchi,et al.  Experimental demonstration of a quantum shutter closing two slits simultaneously , 2016, Scientific Reports.

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

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

[28]  Y. Aharonov,et al.  Quantum to Classical Transitions via Weak Measurements and Post-Selection , 2016, 1602.05083.

[29]  D. Struppa,et al.  Finally making sense of the double-slit experiment , 2017, Proceedings of the National Academy of Sciences.

[30]  R. E. Kastner.  Demystifying Weak Measurements , 2017 .

[31]  Eliahu Cohen,et al.  The Two-Time Interpretation and Macroscopic Time-Reversibility , 2017, Entropy.

[32]  Michael Beny,et al.  Faster than Fourier , 2017 .

[33]  Y. Aharonov,et al.  The Case of the Disappearing (and Re-Appearing) Particle , 2016, Scientific Reports.

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

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

[36]  Robert W. Boyd,et al.  Weak-value measurements can outperform conventional measurements , 2017 .

[37]  Y. Aharonov,et al.  Interaction-Free Effects Between Distant Atoms , 2016, Foundations of Physics.