Experimental nonlocality-based randomness generation with nonprojective measurements

We report on an optical setup generating more than one bit of randomness from one entangled bit (i.e., a maximally entangled state of two qubits). The amount of randomness is certified through the observation of Bell nonlocal correlations. To attain this result we implemented a high-purity entanglement source and a nonprojective three-outcome measurement. Our implementation achieves a gain of 27% of randomness as compared with the standard methods using projective measurements. Additionally, we estimate the amount of randomness certified in a one-sided device-independent scenario, through the observation of Einstein-Podolsky-Rosen steering. Our results prove that nonprojective quantum measurements allow extending the limits for nonlocality-based certified randomness generation using current technology.

Figure 1

Device-independent randomness generation scenario: A user applies uncharacterized measurements $x$ and $y$ to two devices A and B, obtaining outcomes $a$ and $b$, respectively. In the experiment, the user assumes that the state of the two devices A and B is the reduced state of a pure tripartite quantum state $|\mathrm{\Psi }\rangle$ correlated with an adversarial party, Eve, who holds device $\text{E}$. No further assumption is made on Eve, who could have a complete description not only of this quantum state, but also of all the measurements performed on it. In order to guess the outcomes produced in the experiment, Eve applies a measurement to her device $\text{E}$ that produces outcomes $e$. Without loss of generality, this outcome can be seen as Eve's guess on the user's results.

Figure 2

(a) Our experimental setup is composed of an ultrabright parametric down-conversion source (see main text) generating a near-perfect $|{\psi }^{-}\rangle =\left(\right|HV\rangle -|VH\rangle )/\sqrt{2}$ polarization state, followed by polarization measurements in each photon. The measurements $x,y=1,2,3$ have binary outcomes and are implemented using a quarter-wave plate (QWP), a HWP, and a PBS, followed by avalanche photodiode detectors (APDs). A removable mirror (RM) allows one to select between measurements $x=1,2,3$ and $x=4$. The fourth and nonprojective measurement, $x=4$, performed by device A is implemented by a double-path Sagnac interferometer. (b) Bloch sphere representation of the measurements performed in A and B. The measurements labeled by $x,y=1,2,3$ are given by symmetrically spaced two-outcome (projective) measurements in the $x-z$ plane, and correspond to the settings required to maximally violate the chained Bell inequality [12]. Measurement $x=4$ has three outcomes, corresponding to Bloch vectors equally spaced in the $x-z$ plane.

Figure 3

(a) The Sagnac interferometer used to implement the three-outcome POVM. (b) shows the corresponding quantum circuit.