Edited by Yakir Aharonov, Tel Aviv University, Tel Aviv, Israel, and approved December 15, 2010 (received for review April 28, 2010)
Conceptual representation of the experiment. A “signal” photon is prepared with an arbitrary linearly polarized state using a half waveplate (λ/2), 
. A weak measurement of the polarization is then made (
) by interacting the signal photon with a “meter” photon via a C-Sign gate, which operates via a measurement-induced nonlinearity (14, 25–29). Conditional on detecting a single photon in each of the two output modes (a coincidence measurement) the gate ideally performs the operation 
on the two-qubit polarization Hilbert space 
, where 
(
) is the 1-qubit identity (Pauli 
) operator and |H〉 = |0〉, |V〉 = |1〉. See the main text for a full description of 
, 
, and 
and Materials and Methods for more experimental details.
Variation of the weak value, WV (▾), and the Leggett–Garg parameter B (•) for a range of input states |σin〉 parametrized by θ. Postselection is on the diagonal state |D〉, and the measurement strength is K = 0.5445 ± 0.0083. Error bars show the standard deviation and arise from poissonian counting statistics. (A) B parameter using 
. (B) B parameter 
. Solid lines are the theoretical predictions from Eqs. 4 and 2. The horizontal lines at ± 1 indicate the limits of the eigenspectrum of 
. Bmax = 1.312 ± 0.022.
As for Fig. 2, except now K = 0.1598 ± 0.0091. Error bars are larger than in Fig. 2 because of poorer statistics due to reduced postselection probability. (A) B parameter formed with 
. (B) B parameter from 
. Solid lines are the theoretical predictions from Eqs. 4 and 2. Bmax = 1.436 ± 0.053.
Comparison of the Leggett–Garg parameter (B) for a range of input states |σin〉, for the measurement strengths of Fig. 2, K = 0.5445 ± 0.0083 (•), and Fig. 3 K = 0.1598 ± 0.0091 (▴). As before, error bars show the standard deviation and arise from poissonian counting statistics. The range of violation of the LGI is larger when the measurement is less intrusive. The red dashed line is the theoretical result for a zero strength measurement, where the LGI would be violated for all states between |H〉 and |V〉. Note that even with a moderate strength of K = 0.1598 ± 0.0091, we cover most of this range.
Schematic of experimental setup. See Experimental Details for a complete description of the experiment. The calcite beam displacers are in the setup for other experiments. They are not integral to the current experiment and are included here for completeness. The ϕ waveplate is used to adjust the relative phase between the beam displacer interferometers and is an artifact of having the beam displacers.
The three correlation functions that comprise the generalized Leggett–Garg correlation function for a range of input states |σin〉 parametrized by θ. The measurement strength is K = 0.5445 ± 0.0083. Error bars show the standard deviation and arise from poissonian counting statistics.
The three correlation functions that comprise the generalized Leggett–Garg correlation function for a range of input states |σin〉 parametrized by θ. The measurement strength is K = 0.1598 ± 0.0091. Error bars show the standard deviation and arise from poissonian counting statistics.
