Experimental Full Network Nonlocality with Independent Sources and Strict Locality Constraints

Nonlocality arising in networks composed of several independent sources gives rise to phenomena radically different from that in standard Bell scenarios. Over the years, the phenomenon of network nonlocality in the entanglement-swapping scenario has been well investigated and demonstrated. However, it is known that violations of the so-called bilocality inequality used in previous experimental demonstrations cannot be used to certify the nonclassicality of their sources. This has put forward a stronger concept for nonlocality in networks, called full network nonlocality. Here, we experimentally observe full network nonlocal correlations in a network where the source-independence, locality, and measurement-independence loopholes are closed. This is ensured by employing two independent sources, rapid setting generation, and spacelike separations of relevant events. Our experiment violates known inequalities characterizing nonfull network nonlocal correlations by over 5 standard deviations, certifying the absence of classical sources in the realization.

Figure 1

A network with sources (blue circles) distributing physical systems (blue arrows) to three nodes Alice, Bob, and Charlie, represented as $A$, $B$, and $C$ (gray squares). $(x,a)$ and $(z,c)$ are Alice’s and Charlie’s inputs and outputs. Bob performs a joint measurement on his systems yielding outcomes $b$. (a) BLHV model, where each source distributes a different LHV (${\lambda }_1$ and ${\lambda }_2$). (b) Test for FNN, where the model to be discarded consists of one LHV $\lambda$ and a general nonlocal source (NS).

Figure 2

Experimental realization. (a) Overview of our quantum network with two independent sources ($S_1$ and $S_2$) and three nodes (Alice, Bob, and Charlie, represented as $A$, $B$, and $C$). Geographic picture is taken from Google Maps, ©2022 Google [35]. (b) By pumping a periodically poled MgO doped lithium niobate (PPMgLN) crystal in a Sagnac loop, photon pairs in the state $|\phi {⟩}_i=\cos 2{\theta }_i|HH⟩+\sin 2{\theta }_i|VV⟩$ are created via SPDC in each source, where ${\theta }_i$ is the angle of the ${\mathrm{HWP}}_i$ mounted on a motorized rotator. The pulse pattern generator (PPG) in $S_1$ acts as a master clock for synchronizing all devices (see Refs. [19, 34] for details). (c) Bob performs a partial Bell state measurement [36] and his photon detection events are real-time analyzed and recorded by a field-programmable gate array (FPGA). (d) Alice and Charlie measure their photons according to the inputs from their private quantum random number generators (QRNGs). Their detection events and setting choices are recorded by a time-to-digital converter (TDC). See Ref. [29] for more details. IM, intensity modulator; EDFA, erbium-doped fiber amplifier; PC, polarization controller; DM, dichroic mirror; OPM, off-axis parabolic mirror; DWDM, dense wavelength-division multiplexer; FBG, fiber Bragg grating; PBS, polarizing beam splitter; HWP, half-wave plate; QWP, quarter-wave plate; BS, beam splitter; SNSPD, superconducting nanowire single photon detector; FR, Faraday rotator; PM, electro-optic phase modulator.

Figure 3

Space-time configuration in each experimental trial. (a)–(c) Space-time diagrams of the relationship between important events in the nodes, as displayed in the boxes. Blue vertical bars in each space-time diagram denote the time elapsing for the relevant events, with start and end marked by circles and horizontal lines, respectively. (a) Left, middle, and right panels split by red dashed lines: space-time analysis between ${\mathrm{QRNG}}_A$ and $S_1$, space-time analysis between $S_1$ and $S_2$, and space-time analysis between $S_2$ and ${\mathrm{QRNG}}_C$. (b) Space-time analysis between ${\mathrm{QRNG}}_A$ and ${\mathrm{QRNG}}_C$, and spacelike separations between ${\mathrm{QRNG}}_A$ (${\mathrm{QRNG}}_C$) and $M_C$ ($M_A$), and between $S_1$ ($S_2$) and $M_C$ ($M_A$). (c) Space-time analysis between $M_B$ and ${\mathrm{QRNG}}_A$ (${\mathrm{QRNG}}_C$). All the space-time relations are drawn to scale. For more details see Ref. [29].

Figure 4

Experimental results of the FNN witness as functions of the rotation angle ${\theta }_i$ in ${\mathrm{S}}_i$. (a) FNN witness as a function of the angle ${\theta }_1$ when $|\phi {⟩}_2=|{\mathrm{\Phi }}^{+}⟩$. (b) FNN witness as a function of the angle ${\theta }_2$ when $|\phi {⟩}_1=|{\mathrm{\Phi }}^{+}⟩$. Error bars indicate one standard deviation.