Research ArticlePHYSICS

Entanglement classifier in chemical reactions

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Science Advances  02 Aug 2019:
Vol. 5, no. 8, eaax5283
DOI: 10.1126/sciadv.aax5283
  • Fig. 1 Results of two different measurements.

    Ideal results of measurement Z (top) and measurement Z+X2 (bottom). The results of measurement Z (top) are calculated from (30) (Fig. 4, A and B). The blue line fH(θ) represents the scattering angle distribution of particles at state ∣H〉, and the red line fV(θ) represents the scattering angle distribution of particles at state ∣V〉. For measurement Z+X2, its two eigenstates are ΨR+ and ΨR. We assume that the scattering angle distribution f±(θ) of ΨR+ and ΨR satisfy the Gaussian distribution. f+(θ) ∝ exp [ − (θ − 30)2/402] (blue line in the bottom figure); f(θ) ∝ exp [− (θ − 150)2/402] (red line in the bottom figure).

  • Fig. 2 Sketch of the experiment design.

    (A) HD molecules are prepared in the state ∣v = 1, j = 2, m = 0〉 using Stark-induced adiabatic Raman passage (SARP) (30). Then, we can divide them into two molecular beams (two groups). If we apply the Pumps and Stokes electric field along the y axis, then HD in group I is set at state ∣H〉 (orientation of HD is along the y axis, parallel to the direction of its propagation). The molecule HD in group II is set at state ∣V〉 (orientation of HD is along the z axis, norm to the direction of its propagation). One molecule from group I and another from group II are combined together, and then, HD pairs are prepared at different initial states (if we do nothing, then these pairs will stay on a mixed state ∣H〉 ⊗ ∣ V〉). (B) The specific prepared state will go through two channels, molecule in channel I will scatter with H2 clusters, where the bond axis of H2 is distributed isotropically. (C) Sensors (orange) are used to detect scattered particles and count numbers for each angle (Z measurement). Molecules that are not scattered will go to another sensor (gray), by which they will be measured on the eigenstates ∣ + 〉 and ∣ − 〉 (X measurement). (D) In channel II, we set another experiment, so that scattered prepared HD molecules with isotropically distributed H2 clusters are measured under Z+X2, while the others are measured under ZX2.

  • Fig. 3 Simulation results of the scattering experiments.

    The figure shows histograms of the simulation count results (z axis in the figure) as a function of different measures in channel I and channel II. Row 1: The spectrum for the separable state ∣HH〉, both HD molecules are in the state ∣H〉. Row 2: The spectrum for separable state ∣VV〉. Row 3: The spectrum for the superposition state ∣ + + 〉, where +=12(H+D). Row 4: The spectrum for the superposition state ∣ − − 〉, where =12(HD). Rows 5, 6, and 7: The spectrum for the Werner state ρw(p). When p = 1, the prepared pairs are at the Bell state 12(HD+DH).

  • Fig. 4 Theory and simulation results for E of particle pairs at different Werner state ρw(p).

    To calculate the integral, we divided scattering angles into 18 slots (10° per slot). We studied 1 × 106 particles in simulation, and possibility to be scattered is set as 0.4.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/8/eaax5283/DC1

    Section SA. Bell’s inequality for continuous measurement results

    Section SB. Details of the simulation method

    Section SC. An example of spin 12 particles

    Fig. S1. Sketch of Bell’s experiment of spin 12 particles.

    Fig. S2. Simulation result (1z2z).

    Fig. S3. Simulation result (1z2x).

    Fig. S4. Simulation result (1x2z).

    Fig. S5. Simulation result (1x2x).

    Fig. S6. Simulation result (Werner state, ρ = 0.6).

    References (3840)

  • Supplementary Materials

    This PDF file includes:

    • Section SA. Bell’s inequality for continuous measurement results
    • Section SB. Details of the simulation method
    • Section SC. An example of spin 12 particles
    • Fig. S1. Sketch of Bell’s experiment of spin 12 particles.
    • Fig. S2. Simulation result (1z2z).
    • Fig. S3. Simulation result (1z2x).
    • Fig. S4. Simulation result (1x2z).
    • Fig. S5. Simulation result (1x2x).
    • Fig. S6. Simulation result (Werner state, ρ = 0.6).
    • References (3840)

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