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arXiv:0807.4906 · Physical Review A

Linear-optical hyperentanglement-assisted quantum error-correcting code

Mark M. Wilde, Dmitry B. Uskov

Published Feb 5, 2009• 31 citations
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Abstract

We propose a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code. The code is hyperentanglement assisted because the shared entanglement resource is a photonic state hyperentangled in polarization and orbital angular momentum. It is possible to encode, decode, and diagnose channel errors using linear-optical techniques. The code corrects for polarization ``flip'' errors and is thus suitable only for a proof-of-principle experiment. The encoding and decoding circuits use a Knill-Laflamme-Milburn-like scheme for transforming polarization and orbital angular momentum photonic qubits. A numerical optimization algorithm finds a unit-fidelity encoding circuit that requires only three ancilla modes and has success probability equal to 0.0097.

DOI
10.1103/physreva.79.022305

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We present a technique for hyperentangled Bell-state analysis that only relies on linear optics and is assisted by auxiliary entangled states. This technique can be used to implement hyperdense coding with an experimentally realizable two-photon state hyperentangled in polarization and two longitudinal-momentum degrees of freedom. The 16 hyperentangled states in the first two degrees of freedom are classified into 12 groups with the help of the third degree of freedom. This allows the transmission of 3.58 bits/photon via our hyperdense coding scheme. We also generalize our technique to nnn-qubit hyperentangled Bell-state analysis assisted by additional auxiliary entangled states. We show that given nnn degrees of freedom, the 4n{4}^{n}4n hyperentangled Bell states can be separated via linear optics into ${x}_{k}={2}^{n+k+1}\ensuremath{-}{2}^{2k}$ groups with the help of $k\phantom{\rule{4pt}{0ex}}(k\ensuremath{\le}n)$ ancillary entangled states. When k=nk=nk=n, all 4n{4}^{n}4n hyperentangled states can be distinguished. Our results are useful for quantum information processing based on hyperentanglement.
We show that the KLM scheme [Knill, Laflamme, and Milburn, Nature 409, 46 (2001)] can be implemented using polarization encoding, thus reducing the number of path modes required by half. One of the main advantages of this new implementation is that it naturally incorporates a loss detection mechanism that makes the probability of a gate introducing a non-detected error, when non-ideal detectors are considered, dependent only on the detector dark-count rate and independent of its efficiency. Since very low dark-count rate detectors are currently available, a high-fidelity gate (probability of error of order ${10}^{\ensuremath{-}6}$ conditional on the gate being successful) can be implemented using polarization encoding. The detector efficiency determines the overall success probability of the gate but does not affect its fidelity. This can be applied to the efficient construction of optical cluster states with very high fidelity for quantum computing.
Entanglement in high-dimensional quantum systems, where one or more degrees of freedom of light are involved, offers increased information capacities and enables new quantum protocols.Here, we demonstrate a functional source of high-dimensional, noise-resilient hyperentangled states encoded in time-frequency and vector vortex structured modes, which in turn carry single-particle entanglement between polarization and orbital angular momentum.Pairing nonlinearity-engineered parametric downconversion in an interferometric scheme with spin-to-orbital-angular-momentum conversion, we generate highly entangled photon pairs at telecom wavelength that we characterize via two-photon interference and quantum state tomography, achieving near-unity visibilities and fidelities.While hyperentanglement has been demonstrated before in photonic qubits, here we present a rich entanglement structure involving spectrally and spatially structured light, where three different forms of entanglement coexist in the same biphoton state.
Quantum erasure-correcting code, which corrects the erasure in the transmission of quantum information, is an important protocol in quantum information. In the continuous variable regime, the feed-forward technique is needed for realizing quantum erasure-correcting code. This feed-forward technique involves optic-electro and electro-optic conversions, limiting the bandwidth of quantum erasure-correcting code. Moreover, in the previous continuous variable quantum erasure-correcting code, only two modes are protected against erasure, limiting the applications of quantum erasure-correcting code in high-capacity quantum information processing. In this Letter, by utilizing the orbital angular momentum (OAM) multiplexed entanglement in the encoding part and replacing the feed-forward technique with OAM mode-matched phase-sensitive amplifier in the decoding part, we experimentally demonstrate a scheme of OAM multiplexed deterministic all-optical quantum erasure-correcting code. We experimentally demonstrate that four orthogonal modes can be simultaneously protected against one arbitrary erasure. Our results provide an all-optical platform to implement quantum erasure-correcting code and may have potential applications in implementing all-optical fault-tolerant quantum information processing.