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arXiv:2303.06773 · Physical Review A

Protecting classical-quantum signals in free-space optical channels

Eduardo Villaseñor, Matthew S. Winnel, Timothy C. Ralph, Ryan Aguinaldo, Jonathan Green, Robert Malaney

Published Jun 30, 2023• 0 citations
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Abstract

Due to turbulence and tracking errors, free-space optical channels involving mobile transceivers are characterized by a signal's partial loss or complete erasure. This work presents an error-correction protocol capable of protecting a signal passing through such channels by encoding it with an ancillary entangled bipartite state. Beyond its ability to offer protection under realistic channel conditions, our protocol has the ability to transmit both a quantum state and a classical symbol using the same encoded state. We show how the protocol can improve the fidelity of transmitted coherent states over a wide range of losses and erasure probabilities relative to nonencoded direct transmission. In addition, the use of ancillary non-Gaussian entangled bipartite states in the signal encoding is considered, showing how this can increase performance. Finally, we briefly discuss the application of our protocol to the transmission of more complex input states, such as multimode entangled states.

DOI
10.1103/physreva.107.062616

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We present a protocol which allows for arbitrary optical quantum states to simultaneously carry and transmit classical data, without sacrificing the integrity of either the quantum or classical information. Our scheme encodes classical information via displacements in the phase space prior to transmission and retrieves each classical symbol via a Gaussian continuous-variable teleportation. The original quantum state is then restored by guessing the the original displacement and performing the appropriate inverse operation. In the limit of sufficiently high classical signal and high squeezing, we show that our scheme is capable of perfectly reconstructing both the input classical signal and the input quantum state without loss of coherence. An example is given in terms of the transmission of a dual-rail Bell state.
A significant hurdle for quantum information and processing using bosonic systems is stochastic phase errors which occur as the photons propagate through a channel. These errors will reduce the purity of states passing through the channel and therefore reduce the channels capacity. We present a scheme of passive linear optical unitary averaging for protecting unknown Gaussian states transmitted through an optical channel. The scheme reduces the effect of phase noise on purity, squeezing, and entanglement, thereby enhancing the channel via a probabilistic-error-correcting protocol. The scheme is robust to loss and typically succeeds with high probability. We provide both numerical simulations and analytical approximations tailored for relevant parameters with the improvement of practical and current technology. We also show the asymptotic nature of the protocol, highlighting both current and future relevance.
Free-space optical (FSO) links supporting spatial multiplexing provide a natural physical realization of Quantum MIMO channels. We develop a first-principles model for Quantum MIMO channels derived directly from wave-optical propagation through three-dimensional atmospheric turbulence. The framework explicitly accounts for intermodal crosstalk, finite detection apertures, and the system-bath separation induced by spatial-mode projection. We distinguish between distinguishable and indistinguishable photon regimes, showing that indistinguishability leads to intrinsically many-body interference effects described by matrix permanents. To obtain a completely positive and trace-preserving logical description, we introduce an erasure-extended encoding in which turbulence-induced leakage and photon loss are mapped to flagged erasure states. The resulting Quantum MIMO channel naturally reduces to a correlated n-qubit erasure channel, with correlations arising from the shared turbulent medium. Limiting regimes in which correlated Pauli channels emerge as effective approximations are also identified.
We reexamine a non-Gaussian quantum error-correction code designed to protect optical coherent-state qubits against errors due to an amplitude-damping channel. We improve on a previous result [R. Wickert, N. K. Bernardes, and P. van Loock, Phys. Rev. A 81, 062344 (2010)] by providing a tighter upper bound on the performance attained when considering realistic assumptions, which constrain the operation of the gates employed in the scheme. The quantitative characterization is performed through measures of fidelity and concurrence, the latter obtained by employing the code as an entanglement distillation protocol. We find that, when running the code in fully deterministic error-correction mode, direct transmission can only be beaten for certain combinations of channel and input state parameters. In contrast, in error-detection mode, the usage of higher repetition encodings remains beneficial throughout, however, at the expense of diminishing success probabilities.