# Quantum Error Correction Continuous Variable States Against Gaussian Noise

Braunstein discovered a highly **efficient five-wave-packet code theoretically in 1998,** its linear optical construction was not proposed26. After error correction, the measured noise of the output state with the squeezed ancilla modes (red line) is below that using coherent states as the ancilla modes (blue line).Figure 4: The Phys. J. http://vealcine.com/quantum-error/quantum-error-correction-with-degenerate-codes-for-correlated-noise.php

Rev. Phys. 4, 915–918 (2008).ISICASArticle38.Van Loock, P. Walker and S. If the gain of the NLA is sufficiently large and the gain of the output displacement is chosen correctly, the effective channel is a lossy channel of higher transmission than the

From Fig. 3(a,b), we can see that the output state is immune from errors appearing in channels 1 and 2. Experimentally feasible quantum erasure-correcting code for continuous variables. A four-channel digital oscilloscope is used to record the DC output of detectors D1–D4. The QEC code is implemented only with linear optics operations and four ancilla squeezed states of light.

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- A CV QEC scheme against Gaussian noise with a non-Gaussian operation of photon counting has been also theoretically analyzed30.
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- Experimental demonstration of topological error correction.
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et **al. **Lett. 81, 2152–2155 (1998).ISICASArticle7.Knill, E., Laflamme, R., Martinez, R. & Negrevergne, C. C. & van Loock, P. Superconducting quantum circuits at the surface code threshold for fault tolerance.

Experimental implementation of a concatenated quantum error-correcting code. Distinguishing two single-mode Gaussian states by homodyne detection: an information-theoretic approach. When the error occurs in the channel 3, 4 or 5, the output state will be stained by the error and we need to implement the feedforward of the measurement results.Table Phys.

Cyan lines: the noises on amplitude (x) and phase (p) components of output state before error correction. C. We explore the theoretical bounds of the protocol as well as the expected performance given current knowledge and technology.Received 22 May 2011DOI:https://doi.org/10.1103/PhysRevA.84.022339©2011 American Physical SocietyAuthors & Affiliations T. The encoded five modes areFrom equation **(4) we can** see, the input state is partially encoded on channels 3, 4 and 5 , and by means of the designed beam-splitter network,

L. Please try the request again. Phys. 4, 919–923 (2008).CASArticle37.Hage, B. Generally, the stochastic error model is described by38where the input state Win(x, p) is transformed into a new state Werror(x, p) with probability γ or it remains unchanged with probability 1 − γ.

When the used ancilla modes are perfect squeezed states, the output state will totally overlap with the input vacuum state. check my blog The aim of quantum error correction (QEC) is to eliminate or, at least, reduce the hazards resulting from the imperfect channels and to ensure transmission of quantum states with high fidelity1. M. & Cleland, A. Mod.

L. Experimental **quantum error** correction. A. & Braunstein, S. this content J.

Phys. Res. No-Go theorem for Gaussian quantum error correction.

## However, the proposed five-wave-packet CV QEC code has not been experimentally demonstrated so far.Based on the approach outlined by T.

Entanglement-assisted quantum error correction with linear optics. Lett. 102, 120501 (2009).CASPubMedArticle35.Heersink, J. The correlation noises of quadrature components among the encoded five wave-packets are expressed by , , , , and . Rev.

Lett. 77, 198–202 (1996).ISICASPubMedArticle4.Dennis, E., Landahl, A., Kitaev, A. & Preskill, J. A. R. have a peek at these guys Gaussian quantum information.

A. Rev. et al. Rev.

By sweeping the phase of the error wave packet with the piezoelectric translator (PZT) attached on a reflection mirror, a quasi-random displacement error is added on one of the five channels. A variety of discrete variable QEC protocols, such as nine-qubit code2, five-qubit code3, topological code4,5, have been suggested and the experiments of QEC have been realized in different physical systems, such