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arXiv:1308.2102 · Physical Review Letters

Gaussian Error Correction of Quantum States in a Correlated Noisy Channel

Mikael Lassen, Adriano Berni, Lars S. Madsen, Radim Filip, Ulrik L. Andersen

Published Oct 29, 2013• 32 citations
arXivHTMLPDF

Abstract

Noise is the main obstacle for the realization of fault-tolerant quantum information processing and secure communication over long distances. In this work, we propose a communication protocol relying on simple linear optics that optimally protects quantum states from non-Markovian or correlated noise. We implement the protocol experimentally and demonstrate the near-ideal protection of coherent and entangled states in an extremely noisy channel. Since all real-life channels are exhibiting pronounced non-Markovian behavior, the proposed protocol will have immediate implications in improving the performance of various quantum information protocols.

DOI
10.1103/physrevlett.111.180502

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Noise is the main obstacle for the realization of fault-tolerant quantum information processing and secure communication over long distances. In this work, we propose a communication protocol relying on simple linear optics that optimally protects quantum states from non-Markovian or correlated noise. We implement the protocol experimentally and demonstrate the near-ideal protection of coherent and entangled states in an extremely noisy channel. Since all real-life channels are exhibiting pronounced non-Markovian behavior, the proposed protocol will have immediate implications in improving the performance of various quantum information protocols.
The task of protecting quantum entanglement is crucial for quantum communication. Conventionally, correlated noise correction requires an electro-optic modulation process, which limits the application of such correction schemes in constructing broadband quantum communication. Here, we experimentally demonstrate a scheme of all-optical entanglement recovery in a correlated noisy channel without electro-optic modulation. In our scheme, the correlated noisy channel is enabled by an Einstein−Podolsky−Rosen entangled state, a low-noise parametric amplifier, and a beam splitter, thereby avoiding electro-optic conversion. Quantum entanglement is destroyed after one half of the quantum entangled state passes through the noisy channel. Such quantum entanglement can be recovered in the auxiliary noisy channel which shares correlated noise with the noisy channel. Our results pave the way for deterministically implementing all-optical quantum secure communication.
Noise is an important factor that influences the reliability of information acquisition, transmission, processing, and storage. In order to suppress the inevitable noise effects, a fault-tolerant information processing approach via quantum weak measurement is proposed, where pairwise orthogonal postselected measurement bases with various tiny angles and optimal compositions of measured results are chosen as a decoding rule. The signal to be protected can be retrieved with a minimal distortion after having been transmitted through a noisy channel. Demonstrated by typical examples of encoding signal on two-level superposition state or Einstein-Podolsky-Rossen state transmitted through random telegraph noise and decoherence noises channel, the mean squared error distortion may be close to 000 and the fault-tolerant capability could reach 111 with finite quantum resources. To verify the availability of the proposed approach, classic coherent light and quantum coherent state are used for encoding information in the experiment. Potentially, the proposed approach may provide a solution for suppressing noise effects in long-distance quantum communication, high-sensitivity quantum sensing, and accurate quantum computation.
One of the consequences in the distribution of quantum states over a long distance is that, since resulting quantum states are noisy due to the intervention of an environment, a measurement setting should be re-aligned to optimize detection events, for which additional experimental resources such as quantum tomography of a channel or resulting states is necessary. In this work, we present a protocol for protecting an optimal measurement setup without verifying a channel. A receiver does not have to revise the measurement prepared in a noiseless scenario since it would remain optimal for quantum states resulting from an unknown and noisy channel. The measurement protection protocol realizes a supermap describing transformations over quantum channels and is experimentally feasible as it only applies local unitary transformations before and after the transmission. We present experimental proof-of-principle demonstrations of the measurement protection protocol. We also apply the measurement protection to a prepare-and-measure protocol, the Bennett-Brassard 1984 (BB84) protocol, and find that preserving an optimal measurement can suppress quantum-bit error rates, allowing the protocol to tolerate an even higher noise during transmission. The BB84 protocol with the measurement protection is experimentally demonstrated with the polarization encoding on photonic qubits.
A quantum communication network can be constructed by distributing a multipartite entangled state to space-separated nodes. Entangled optical beams with highest flying speed and measurable brightness can be used as carriers to convey information in quantum communication networks. Losses and noises existing in real communication channels will reduce or even totally destroy entanglement. The phenomenon of disentanglement will result in the complete failure of quantum communication. Here, we present the experimental demonstrations on the disentanglement and the entanglement revival of tripartite entangled optical beams used in a quantum network. We experimentally demonstrate that symmetric tripartite entangled optical beams are robust in pure lossy but noiseless channels. In a noisy channel, the excess noise will lead to the disentanglement and the destroyed entanglement can be revived by the use of a correlated noisy channel (non-Markovian environment). The presented results provide useful technical references for establishing quantum networks.
The creation of a quantum network is an important goal of quantum information processing. Long distance quantum communication with high fidelity is the main obstacle in achieving this goal. A scheme to transmit qubits without fidelity decrease over the noisy channel is presented. Using the idea of ‘time-bin entanglement’, the scheme works without any auxiliary particles and there is no resources increase with the length of the channel. A protocol proposed by Kalamidas [18] is suitable to realize our scheme with the current experimental technology.
Near-term quantum communication protocols suffer inevitably from channel noises, whose alleviation has been mostly attempted with resources such as multiparty entanglement or sophisticated experimental techniques. Generation of multiparty higher dimensional entanglement is not easy. This calls for exploring realistic solutions which are implementable with current devices. Motivated particularly by the difficulty in generation of multiparty entangled states, in this paper, we have investigated error-free information transfer with minimal requirements. For this, we have proposed a new information encoding scheme for communication purposes. The encoding scheme is based on the fact that most noisy channels leave some quantities invariant. Armed with this fact, we encode information in these invariants. These invariants are functions of expectation values of operators. This information passes through the noisy channel unchanged. Pertinently, this approach is not in conflict with other existing error correction schemes. In fact, we have shown how standard quantum error-correcting codes emerge if suitable restrictions are imposed on the choices of logical basis states. As applications, for illustration, we propose a quantum key distribution protocol and an error-immune information transfer protocol.