Realization of entanglement-assisted weak-value amplification in a photonic system

Weak-value amplification has been used to enhance the sensitivity of a linear detector response to small interaction parameters. However, the generation of a large weak value gives rise to reduction in postselection probability, which restricts the feasibility of the weak-value amplification technique. Recently, theoretical works have shown that the use of entanglement can increase the efficiency of the weak-value amplification method. Specifically, it is proven that by entangling $n$ particles of a system, the maximum postselection probability scales quadratically with $n$ [Pang, Dressel, and Brun, Phys. Rev. Lett. 113, 030401 (2014)]. In this work, we demonstrate an experimental realization of entanglement-assisted weak-value amplification in a photonic system, which shows that importing quantum entanglement can indeed improve the efficiency of weak-value amplification.

Figure 1

(a) Experimental setup in correlated case. IF denotes interference filter, BD denotes beam displacer, H denotes half-wave plate, Q denotes quarter-wave plate, and PBS denotes polarizing beam splitter. The single photons, which are produced by generating a pair of photons via spontaneous parametric down conversion (SPDC) with idler photons used as triggers, are prepared into the initial state $|{\psi }_i\rangle =\left(\right|H\rangle +|V\rangle )/\sqrt{2}$ and sent to BD1. Imagine that we look at this setup from the top down; the solid lines represent the upper paths while the dashed lines represent the lower paths. After weak interaction and measurements on the meter observables are performed, postselection and coincidence counting are performed subsequently. H1, H5, H8 are rotated at $\pi /4$, H2 is rotated at $1^{\circ }$, while H3 is rotated at $-1^{\circ }$. Q and H4 combining PBS1 after them are used to make projective measurements on the pointer. (b) The corresponding quantum circuit for realizing weak measurements.

Figure 2

Experimental results. Correlated and uncorrelated cases are compared using weak values in (a) and (b). For every $\epsilon$, the weak values of the two cases are set to be the same in theory. In (c), we compare the postselection probability of the two different cases in the experiment. Black and gray points correspond to the probability of correlated and uncorrelated cases, black and gray lines correspond to the exact probability of correlated and uncorrelated cases, and black dashed line and gray dotted-dashed line correspond to the approximate probability of correlated and uncorrelated cases. Error bars for (a)–(c) are evaluated on the basis of statistical and system errors, and the statistical errors are evaluated on the basis of Poissonian counting statistics. Here, we consider that system errors are mainly caused by various wave-plate errors, and every wave plate has an alignment error of $0.2^{\circ }$. For the system errors, we calculate them by use of error transfer formula. The wave-plate alignment error results in an error for $\epsilon$; as a result, there are error bars in the horizontal direction for each data point. (The quantities which we study, such as the $\epsilon$, the weak value, and the probability, are dimensionless, so we have not used units in the above figures.)

Figure 3

Experimental setup for realizing weak measurements in the uncorrelated case.