Quantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code

Abstract

A fundamental requirement for enabling fault-tolerant quantum information processing is an efficient quantum error-correcting code (QECC) that robustly protects the involved fragile quantum states from their environment [1][2][3][4][5][6][7][8][9][10]. Just as classical errorcorrecting codes are indispensible in today's information technologies, it is believed that QECC will play a similarly crucial role in tomorrow's quantum information systems. Here, we report on the first experimental demonstration of a quantum erasurecorrecting code that overcomes the devastating effect of photon losses. Whereas errors translate, in an information theoretic language, the noise affecting a transmission line, erasures correspond to the in-line probabilistic loss of photons. Our quantum code protects a four-mode entangled mesoscopic state of light against erasures, and its associated encoding and decoding operations only require linear optics and Gaussian resources. Since in-line attenuation is generally the strongest limitation to quantum communication, much more than noise, such an erasure-correcting code provides a new tool for establishing quantum optical coherence over longer distances. We investigate two approaches for circumventing in-line losses using this code, and demonstrate that both approaches exhibit transmission fidelities beyond what is possible by classical means.Quantum information protocols are inevitably affected by noise, which in turn produces errors in the extremely sensitive processed quantum information [1]. Thus, in order to gain the full advantage of quantum information processing, including long-distance quantum communication and fault-tolerant quantum computing [11][12][13], these errors must be efficiently corrected. This can be done by encoding the information in special quantum error-correcting codes, which introduce redundancy and thereby protect the fragile quantum information from environment-induced decoherence. Using such codes, the transmission errors can be diagnosed through so-called syndrome measurements, the results of which are used to correct the corrupted quantum information.Quantum error correcting codes (QECC) were first discovered for discrete variable qubit systems [2][3][4][5][6][7] and later extended to systems where information is encoded into observables with a continuous spectrum [8-10, 14, 15]. Only a few experimental implementations demonstrating quantum error correction have been carried out to date, e.g., in nuclear magnetic resonance systems [16], in an ion-trap system [17], and in a pure optical system [18,19]. All these works have reported on the correction of errors, which are the manifestation of line noise. However, it is very often the loss of photons in a transmission line (corresponding to erasures in an information theoretic language) that is the main obstacle to the survival of quantum coherence.Erasure-correcting codes have long been known in classical coding theory, and their quantum counterparts have also been theoretically developed. The experimental progr...

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