Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
, 115 (25), 250402

Strong Loophole-Free Test of Local Realism

Affiliations

Strong Loophole-Free Test of Local Realism

Lynden K Shalm et al. Phys Rev Lett.

Abstract

We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart and by using fast random number generators and high-speed polarization measurements. A high-quality polarization-entangled source of photons, combined with high-efficiency, low-noise, single-photon detectors, allows us to make measurements without requiring any fair-sampling assumptions. Using a hypothesis test, we compute p values as small as 5.9×10^{-9} for our Bell violation while maintaining the spacelike separation of our events. We estimate the degree to which a local realistic system could predict our measurement choices. Accounting for this predictability, our smallest adjusted p value is 2.3×10^{-7}. We therefore reject the hypothesis that local realism governs our experiment.

Figures

FIG. 1
FIG. 1
Schematic of the entangled photon source. A pulsed 775 nm-wavelength Ti:Sapphire picosecond mode-locked laser running at 79.3 MHz repetition rate is used as both a clock and a pump in our setup. A fast photodiode (FPD) and divider circuit are used to generate the synchronization signal that is distributed to Alice and Bob. A polarization-maintaining single-mode fiber (SMF) then acts as a spatial filter for the pump. After exiting the SMF, a polarizer and half-wave plate (HWP) set the pump polarization. To generate entanglement, a periodically poled potassium titanyl phosphate (PPKTP) crystal designed for Type-II phasematching is placed in a polarization-based Mach-Zehnder interferometer formed using a series of HWPs and three beam displacers (BD). At BD1 the pump beam is split in two paths (1 and 2): the horizontal (H) component of polarization of the pump translates laterally in the x direction while the vertical (V) component of polarization passes straight through. Tilting BD1 sets the phase, ϕ, of the interferometer to 0. After BD1 the pump state is (cos(16°) |H1〉 + sin(16°) |V2〉). To address the polarization of the paths individually, semi-circular waveplates are used. A HWP in path 2 rotates the polarization of the pump from vertical (V) to horizontal (H). A second HWP at 0° is inserted into path 1 to keep the path lengths of the interferometer balanced. The pump is focused at two spots in the crystal, and photon pairs at a wavelength of 1550 nm are generated in either path 1 or 2 through the process of spontaneous parametric downconversion. After the crystal, BD2 walks the V-polarized signal photons down in the y direction (V1a and V2a) while the H-polarized idler photons pass straight through (H1b and H2b). The xy view shows the resulting locations of the four beam paths. HWPs at 45° correct the polarization while HWPs at 0° provide temporal compensation. BD3 then completes the interferometer by recombining paths 1 and 2 for the signal and idler photons. The two downconversion processes interfere with one another, creating the entangled state in Eq. (2). A high-purity silicon wafer with an anti-reflection coating is used to filter out the remaining pump light. The idler (signal) photons are coupled into a SMF and sent to Alice (Bob).
FIG. 2
FIG. 2
Receiver station setup for Alice and Bob. A photon arrives from the source. Two half-wave plates (HWP), a quarter-wave plate (QWP), a Pockels cell (PC), and two plate polarizers together act to measure the polarization state of the incoming photon. The polarization projection is determined by a random bit from XORing the outputs of two random number generators (RNG1 and RNG2) with pre-determined pseudorandom bits (RNG3). If the random bit is “0”, corresponding to measurement setting a (b) for Alice (Bob), the Pockels cell remains off. If the random bit is “1”, corresponding to measurement setting a′ (b′) for Alice (Bob), then a voltage is applied to the Pockels cell that rotates the polarization of the photons using a fast electro-optic effect. The two plate polarizers have a combined contrast ratio > 7000 : 1. The photons are coupled back into a single-mode fiber (SMF) and detected using a superconducting nanowire single-photon detector (SNSPD). The signal is amplified and sent to a time-tagging unit where the arrival time of the event is recorded. The time tagger also records the measurement setting, the synchronization signal, and a one pulse-per-second signal from a global positioning system (GPS). The pulse-per-second signal provides an external time reference that helps align the time tags Alice and Bob record. A 10 MHz oscillator synchronizes the internal clocks on Alice’s and Bob’s time taggers. The synchronization pulse from the source is used to trigger the measurement basis choice.
FIG. 3
FIG. 3
Minkowski diagrams for the spacetime events related to Alice (A) and the source (S) and Bob (B) and the source (a), and Alice and Bob (b). All lightcones are shaded blue. Due to the geometry of Alice, Bob, and the source, more than one spacetime diagram is required. In a) the random number generators (RNGs) at Alice and Bob must finish picking a setting outside the lightcone of the birth of an entangled photon pair. A total of 15 pump pulses have a chance of downconverting into an entangled pair of photons each time the Pockels cells are on. The events related to the first pulse are not spacelike separated, because Alice’s RNG does not finish picking a setting before information about the properties of the photon pair can arrive; pulses 2 through 11 are spacelike separated. As shown in (b), pulses 12 through 15 are not spacelike separated as the measurement is finished by Alice and Bob after information about the other party’s measurement setting could have arrived. In our experiment the events related to pulse 6 are the furthest outside of all relevant lightcones.
FIG. 4
FIG. 4
(a) The positions of Alice (A), Bob (B), and the source (S) in the building where the experiment was carried out. The insets show a magnified (×2) view of Alice’s and Bob’s locations. The white dots are the location of the random number generators (RNGs). The larger circle at each location has a radius of 1 m and corresponds to our uncertainty in the spatial position measurements. Alice, Bob, and the source can be located anywhere within the green shaded regions and still have their events be spacelike separated. Boundaries are plotted for aggregates of one, three, five, and seven pulses. Each boundary is computed by keeping the chronology of events fixed, but allowing the distance between the three parties to vary independently. In (b) the p-value of each of the individual 15 pulses is shown. Overlayed on the plot are the aggregate pulse combinations used in the contours in (a). The statistical significance of our Bell violation does not appear to depend on the spacelike separation of events. For reference and comparison purposes only, the corresponding number of standard deviations for a given p-value (for a one-sided normal distribution) are shown.
FIG. 5
FIG. 5
The p-value for different numbers of aggregate pulses as a function of the excess predictability, ε, in Alice’s and Bob’s measurement settings. Larger levels of predictability correspond to a weakening of the assumption that the settings choices are physically independent of the photon properties Alice and Bob measure. As in Fig. 4(b), the p-value equivalent confidence levels corresponding to the number of standard deviations of a one-sided normal distribution are shown for reference.

Similar articles

See all similar articles

Cited by 44 PubMed Central articles

See all "Cited by" articles
Feedback