Research ArticleQUANTUM INFORMATION

Robust bidirectional links for photonic quantum networks

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Science Advances  08 Jan 2016:
Vol. 2, no. 1, e1500672
DOI: 10.1126/sciadv.1500672
  • Fig. 1 Optical quantum network.

    (A) A quantum network where each QIP module is connected to other modules through an input port and an output port. (B) These input/output links can be constructed with our method using polarization-maintaining (PM) fibers. Here, we show the links that can transfer single qubits. To send entangled states of multiple qubits, we can either include more such transmission links or send through the same link sequentially.

  • Fig. 2 Experimental setup.

    (A) The full setup for entanglement distribution over a pair of 120-m-long PM fibers. Part of the entangled photon is kept by Alice’s laboratory; another part of the entangled pair enters the interferometric unit. The photons are finally detected by single-photon avalanche detectors (SPADs) with 3-nm interference filters (IFs) in front of them. (B) The two fibers are bundled together to maximize error correlation.

  • Fig. 3 Quantum information transmission through noisy channels.

    (A) In the standard quantum channel theory, where channels are assumed to be independent and uncorrelated, photons can pass through each channel or the same channel one after another, following a tensorial decomposition. (B) In the setting of interferometric activation over optical fibers, a photon, carrying a qubit of information in the polarization basis, can travel through different channels, inducing an extra DOF to compensate for correlated noise through interference.

  • Fig. 4 Experimental results.

    (A) The real part of the experimental matrix χ(s) for a single fiber. (B) The coherent information Embedded Image calculated from χ(s) by scanning θ and λ0, with ϕ = 47π/50. (C) Coherent information of the single fiber as a function of λ0, with θ = 7π/25 and ϕ = 47π/50. The theoretical prediction (black line) agrees with the experimental result (blue line and red dots), which is nearly equal to zero (the black line and the blue line nearly overlap, and only the blue line can be seen). (D) The fidelities of different states passing through the single fiber. (E) The real part of the experimental mean density matrix χ(AB) for the bidirectional use from A (left) to B (right). (F) The coherent information calculated from χ(AB) as a function of θ and λ0, with ϕ = 13π/10. (G) Coherent information of the paired fibers as a function of λ0, with θ = 7π/25 and ϕ = 13π/10. The black line represents the theoretical prediction. The blue line and red dots represent the results calculated from χ(AB) (H) The fidelities of different states passing through the paired fibers. (I) The real part of the experimental mean density matrix χ(BA) for the bidirectional use from B (right) to A (left). (J) The coherent information calculated from χ(BA) as a function of θ and λ0, with ϕ = 41π/25. (K) Coherent information of the paired fibers as a function of λ0 with θ = 19π/25 and ϕ = 41π/25. The black line represents the theoretical prediction. The blue line and red dots represent the results calculated from χ(BA) (L) The fidelities of different states passing through the paired fibers. Error bars are estimated from the SD.

  • Fig. 5 Experimental results for the entangled input states with one of the photons passing through the paired PM fibers.

    (A) The fidelities of the photon states with α2 = 0.1, 0.2, 0.5, 0.8, and 0.9. (B) The coherent information with the corresponding input states. (C and D) The components for obtaining the CHSH values when states are transferred (C) from A to B (S = 2.438 ± 0.025) and (D) from B to A (S = 2.542 ± 0.023). Error bars are estimated from the SD.

  • Fig. 6 Different approaches to constructing DFS for optics.

    (A) A standard two-photon approach (16, 23) where entangled states are prepared probabilistically. (B) An alternative two-photon approach (21, 25, 29) where the protected subspace is obtained through postselection of a parity check. (C) A single-photon approach (applicable for arbitrary multiple-photon states) presented in this report where the path DOF is used to construct an effective DFS.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/1/e1500672/DC1

    Dephasing effect of PM optical fibers

    Coherent information

    Single-use channel capacity of the completely dephasing channel

    Reconstruction of the density matrix χ

    Unidirectional transfer

    Fig. S1. Quantum state evolution of unidirectional information transfer in the case where the noise from the two fibers is perfectly correlated.

    Fig. S2. Experimental results for the unidirectional transformation.

    Fig. S3. Experimental results for the entangled input states, with one of the photons passing through the paired PM fibers.

    Phase stabilization

    Fig. S4. Envelope of two-photon coincidence counts by scanning of the piezo position.

    Imaginary part of the density matrix χ

    Related transmission methods

    Fig. S5. Experimental results for the imaginary parts of the density matrixes χ.

    Fig. S6. For postselection free unidirectional transmission of quantum information with a single PM fiber, active components (for example, electronic half-wave plates) and accurate active control systems are needed.

    Fig. S7. For postselection free bidirectional transmission of quantum information with a single PM fiber, active components (for example, electronic half-wave plates) and accurate active control systems are needed.

    Comparison with the active single PM fiber case

  • Supplementary Materials

    This PDF file includes:

    • Dephasing effect of PM optical fibers
    • Coherent information
    • Single-use channel capacity of the completely dephasing channel
    • Reconstruction of the density matrix χ
    • Unidirectional transfer
    • Fig. S1. Quantum state evolution of unidirectional information transfer in the case where the noise from the two fibers is perfectly correlated.
    • Fig. S2. Experimental results for the unidirectional transformation.
    • Fig. S3. Experimental results for the entangled input states, with one of the photons passing through the paired PM fibers.
    • Phase stabilization
    • Fig. S4. Envelope of two-photon coincidence counts by scanning of the piezo position.
    • Imaginary part of the density matrix χ
    • Related transmission methods
    • Fig. S5. Experimental results for the imaginary parts of the density matrixes χ.
    • Fig. S6. For postselection free unidirectional transmission of quantum information with a single PM fiber, active components (for example, electronic half-wave plates) and accurate active control systems are needed.
    • Fig. S7. For postselection free bidirectional transmission of quantum information with a single PM fiber, active components (for example, electronic half-wave plates) and accurate active control systems are needed.
    • Comparison with the active single PM fiber case

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