Experimental three-photon quantum nonlocality under strict locality conditions

Abstract

Quantum correlations are critical to our understanding of nature, with far-reaching technological [1][2][3][4] and fundamental impact. These often manifest as violations of Bell's inequalities [5][6][7][8], bounds derived from the assumptions of locality and realism, concepts integral to classical physics. Many tests of Bell's inequalities have studied pairs of correlated particles; however, the immense interest in multi-particle quantum correlations is driving the experimental frontier to test systems beyond just pairs. All experimental violations of Bell's inequalities to date require supplementary assumptions, opening the results to one or more loopholes, the closing of which is one of the most important challenges in quantum science. Individual loopholes have been closed in experiments with pairs of particles [9][10][11][12][13][14] and a very recent result closed the detection loophole in a six ion experiment [15]. No experiment thus far has closed the locality loopholes with three or more particles. Here, we distribute three-photon Greenberger-Horne-Zeilinger entangled states[16] using optical fibre and free-space links to independent measurement stations. The measured correlations constitute a test of Mermin's inequality [17] while closing both the locality and related freedom-of-choice loopholes due to our experimental configuration and timing. We measured a Mermin parameter of 2.77 ± 0.08, violating the inequality bound of 2 by over 9 standard deviations, with minimum tolerances for the locality and freedom-of-choice loopholes of 264 ± 28 ns and 304 ± 25 ns, respectively. These results represent a significant advance towards definitive tests of the foundations of quantum mechanics[18] and practical multi-party quantum communications protocols [19].In his breakthrough work, John Bell[5] derived upper bounds on the strength of correlations exhibited by local hidden variable (LHV) theories, very general models of nature in which measurement outcomes in one region of space are independent of the events in other space-like separated regions. Quantum mechanical correlations can violate these bounds. Greenberger, Horne, and Zeilinger (GHZ) extended Bell's argument to the scenario with three-particle entangled states, and showed they could manifest violations of local realism in a fundamentally different way [16,20]. The GHZ argument was converted into the form of an inequality by Mermin[17] which we experimentally tested.An ideal Bell inequality experiment requires separating two or more particles by a large distance and making highefficiency local measurements on those particles using randomly chosen settings and comparing these results [21,22]. The first Bell inequality tests were carried out using twophoton cascades in atomic systems [7,8]. Mermin's inequality was violated using three-photon entanglement from a parametric down-conversion source [23]. However, these and the many other Bell experiments that followed are subject to one or more loopholes that could, in principle, be exploited to yield a violat...

Generation of Fresh and Pure Random Numbers for Loophole-Free Bell Tests

“…To be secure, they must close two spacetime loopholes: no basis choice may influence a distant particle (locality loophole), and the entanglement generation must not influence the basis choices (freedom-ofchoice loophole). Current efforts [6,7,[12][13][14] to simultaneously close the detection [4,6,7], locality [3], and freedom-of-choice (FoC) [5,8] loopholes require random number generators (RNGs) with an unprecedented combination of speed, unpredictability, and confidence [15][16][17].Here we combine ultrafast RNG by accelerated laser phase diffusion [18][19][20] with real-time randomness extraction and metrological randomness assurances [21] to produce a RNGs suitable for loophole-free Bell tests. Because the laser phase diffusion is driven by effects, including spontaneous emission, that are unpredictable both in quantum theory and in an important class of stochastic hidden variable theories, the source can be used to address the "freedom-of-choice" loophole [22].…”

Requirements for a loophole-free photonic Bell test using imperfect setting generators

“…Space-like separating the two outcome events enforces outcome independence, and space-like separating each party's independent setting choice event from the opposite party's outcome event enforces setting independence. In this way, the locality loophole is considered to have been closed for photons by the experiments [17][18][19][20][21], and with NV centers by the experiment [22].…”

“…For example, space-like separation of the pair generation from the setting choices eliminates the pair generation as a possible influence. This has been achieved in the experiments [18][19][20][21]. However, again it is not possible to exclude all possible influences in this way, because these could in principle extend arbitrarily far into the past.…”

“…1, where (The relevant space-like separations can only be achieved by using at least three distinct locations. One measurement device may be located at the source [18,19], but then the corresponding setting generator needs to be placed at a distance.) The time duration τ S for a and b must be smaller than τ 1 , and the time for setting generation as well as deployment of the setting (duration τ D ) must be smaller than τ 2 :…”

Pure-state tomography with the expectation value of Pauli operators

“…The red squre represents fidelity of reconstruction using our protocol. Figure 7 depicts a typical scheme for measuring a polarization-encoded n-photon state [19][20][21][22][23][24]. Quarter-and half-waveplates in each photon's path are rotated to choose a separable polarization basis.…”