Robust bidirectional links for photonic quantum networks

Abstract

Optical fibers are widely used as one of the main tools for transmitting not only classical but also quantum information. We propose and report an experimental realization of a promising method for creating robust bidirectional quantum communication links through paired optical polarization-maintaining fibers. Many limitations of existing protocols can be avoided with the proposed method. In particular, the path and polarization degrees of freedom are combined to deterministically create a photonic decoherence-free subspace without the need for any ancillary photon. This method is input state-independent, robust against dephasing noise, postselection-free, and applicable bidirectionally. To rigorously quantify the amount of quantum information transferred, the optical fibers are analyzed with the tools developed in quantum communication theory. These results not only suggest a practical means for protecting quantum information sent through optical quantum networks but also potentially provide a new physical platform for enriching the structure of the quantum communication theory.

Keywords: Bidirectional quantum communication; decoherence-free subspace; polarization-maintaining fiber; quantum capacity.

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 ${\mathcal{I}}_{\mathrm{c}}$ 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.