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Optics Express

Entanglement-enabled decoherence-free transmission of two-color photons through a single mode fiber

Youhei Okawa, Shunsuke Fujisawa, Yuhsuke Yasutake, S. Fukatsu

Published Dec 5, 2023• 6 citations
Publisher

Abstract

We demonstrate decoherence-tolerant transmission of a Bell state through a single-mode fiber (SMF) using the photon frequency degree of freedom. To this end, a slightly non-degenerate polarization-entangled singlet, |Ψ−⟩=(|HV⟩−|VH⟩)/2, is localized at the SMF as the depolarization channel subject to random noise due to incessant fiber bending. Two-photon beats and quantum state tomography jointly verify the absence of collective decoherence, showing that |Ψ−⟩ is the sought-after one-dimensional decoherence-free subspace (DFS) pertaining to SMF. Efficient splitting and combining of photon streams in our DFS help outperform the DFS in time domain. This motivates us to attempt DFS-enabled fault-tolerant fiber transmission of biphoton qubits. Two-photon BB84 protocol is implemented in a polarization-maintaining fiber to which dephasing noise is relevant so that a two-dimensional DFS is appropriate. A low bit error rate 5.4% is achieved by encoding one-qubit information onto the biphoton state in spite of significant polarization fluctuation. Our scalable frequency-based DFS has a natural affinity for wavelength division multiplexing in fiber communication by design and as such is extensible to multi-particle entanglement.

DOI
10.1364/oe.496570

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•Jan 1, 2004•0 citations
We demonstrate decoherence-tolerant transmission of a Bell state through a single-mode fiber (SMF) using the photon frequency degree of freedom. To this end, a slightly non-degenerate polarization-entangled singlet, |Ψ−⟩=(|HV⟩−|VH⟩)/2, is localized at the SMF as the depolarization channel subject to random noise due to incessant fiber bending. Two-photon beats and quantum state tomography jointly verify the absence of collective decoherence, showing that |Ψ−⟩ is the sought-after one-dimensional decoherence-free subspace (DFS) pertaining to SMF. Efficient splitting and combining of photon streams in our DFS help outperform the DFS in time domain. This motivates us to attempt DFS-enabled fault-tolerant fiber transmission of biphoton qubits. Two-photon BB84 protocol is implemented in a polarization-maintaining fiber to which dephasing noise is relevant so that a two-dimensional DFS is appropriate. A low bit error rate 5.4% is achieved by encoding one-qubit information onto the biphoton state in spite of significant polarization fluctuation. Our scalable frequency-based DFS has a natural affinity for wavelength division multiplexing in fiber communication by design and as such is extensible to multi-particle entanglement.
The global quantum network requires the distribution of entangled states over long distances, with substantial advances already demonstrated using polarization. While Hilbert spaces with higher dimensionality, e.g., spatial modes of light, allow higher information capacity per photon, such spatial mode entanglement transport requires custom multimode fiber and is limited by decoherence-induced mode coupling. Here, we circumvent this by transporting multidimensional entangled states down conventional single-mode fiber (SMF). By entangling the spin-orbit degrees of freedom of a biphoton pair, passing the polarization (spin) photon down the SMF while accessing multiple orbital angular momentum (orbital) subspaces with the other, we realize multidimensional entanglement transport. We show high-fidelity hybrid entanglement preservation down 250 m SMF across multiple 2 × 2 dimensions, confirmed by quantum state tomography, Bell violation measures, and a quantum eraser scheme. This work offers an alternative approach to spatial mode entanglement transport that facilitates deployment in legacy networks across conventional fiber.
A phenomenological Hamiltonian of photons in single-mode stochastic fiber depending on the vector of random parameters is proposed. The time dynamics of single-photon density matrix in the basis of states with orthogonal polarizations is considered. The fiber-parameter-averaged quantum bit error rate (QBER) in a sifted quantum key distributed over the BB84 protocol using entangled polarization states of biphotons is found. It is shown that QBER can be significantly reduced even at large dispersions of random fiber parameters. To this end, identically fabricated fibers must be used for quantum channels A and B. The choice of pairs of fiber segments must be correlated, with a correlation coefficient close to unity. This approach is based on a remarkable property of the singlet biphoton state, which is “free of collective decoherence.” A correlated choice of fiber segments for channels A and B reduces significantly QBER, making its value below critical (i.e., equal to 0.11, a level below which a distributed key is accepted for cryptographic purposes).
The global quantum network requires the distribution of entangled states over long distances, with significant advances already demonstrated using polarization, reaching approximately 1200 km in free space and 100 km in optical fiber. While Hilbert spaces with higher dimensionality, e.g., spatial modes of light, allows higher information capacity per photon, such spatial mode entanglement transport requires custom multimode fiber and is limited by decoherence induced mode coupling. Here we circumvent this by transporting multi-dimensional spatial entangled states down conventional single-mode fiber (SMF). We achieve this by entangling the spin-orbit degrees of freedom of a bi-photon pair, passing the polarization (spin) photon down the SMF while accessing multiple orbital angular momentum (orbital) sub-spaces with the other, thereby realizing multi-dimensional spatial entanglement transport. We show high fidelity hybrid entanglement preservation down 250 m of SMF across multiple 2 x 2 dimensions, which we confirm by quantum state tomography and Bell violation measures. This work offers an alternative approach to spatial mode entanglement transport that facilitates deployment in legacy networks across conventional fiber optic links.
We experimentally implement a fault-tolerant quantum key distribution protocol with two photons in a decoherence-free subspace [Phys. Rev. A 72, 050304(R) (2005)]. It is demonstrated that our protocol can yield a good key rate even with a large bit-flip error rate caused by collective rotation, while the usual realization of the Bennett-Brassard 1984 protocol cannot produce any secure final key given the same channel. Since the experiment is performed in polarization space and does not need the calibration of a reference frame, important applications in free-space quantum communication are expected. Moreover, our method can also be used to robustly transmit an arbitrary two-level quantum state in a type of decoherence-free subspace.
Embedding a quantum state in a decoherence-free subspace (DFS) formed by multiple photons is one of the promising methods for robust entanglement distribution of photonic states over collective noisy channels. In practice, however, such a scheme suffers from a low efficiency proportional to transmittance of the channel to the power of the number of photons forming the DFS. The use of a counter-propagating coherent pulse can improve the efficiency to scale linearly in the channel transmission, but it achieves only protection against phase noises. Recently, it was theoretically proposed [Phys. Rev. A 87, 052325(2013)] that the protection against bit-flip noises can also be achieved if the channel has a reciprocal property. Here we experimentally demonstrate the proposed scheme to distribute polarization-entangled photon pairs against a general collective noise including the bit flip noise and the phase noise. We observed an efficient sharing rate scaling while keeping a high quality of the distributed entangled state. Furthermore, we show that the method is applicable not only to the entanglement distribution but also to the transmission of arbitrary polarization states of a single photon.
We propose a distribution scheme of polarization states of a single photon over collective-noise channel assisted with one additional photon in a fixed polarization state. Although the present scheme does not encode the polarization state of a photon to an entangled state of two photons in the decoherence-free subspace, the state is protected against collective noise and extracted by a measurement based on the parity check and the post-selection. This scheme will easily be applied to many quantum communication protocols based on qubits.