Niset-Andersen-Cerf code[1]


Encodes two-mode coherent states \(\{|\alpha\rangle, |\beta\rangle\}\) over two modes into four modes such that the values \((\alpha,\beta)\) are recoverable after a single-mode erasure. There are two variations of the storage procedure: a deterministic protocol that offers recovery against a single mode erasure, and a probabalistic that can protect against multiple errors with post selection. This code is effectively protecting classical information stored in \((\alpha,\beta)\) using quantum operations.


The deterministic protocol protects against a single erasure error on a known mode. This recovers one state perfectly and the other state with fidelity \(F = \frac{1}{1 + e^{-2 r}}\) for an initial EPR pair squeezed with variance \(e^{-2r}\). The probabalistic protocol utilizes post-selection to protect against multiple erasures with state-dependent fidelity.


After an EPR pair preparation, use 2 continuous CNOT and 2 continuous inverse CNOT gates to entangle a bosonic EPR pair with initial states \(|\alpha \rangle\) and \(|\beta \rangle\).Alternate optical encoder using a two-mode squeezed vacuum state and two balanced beam splitters to mix the input coherent states with the EPR pair.


Optical decoder using three beam splitters, electronic gain detectors, and two phase-insensitive amplifiers as described in Ref. [1].


Realized in Ref. [2] in an optical system with 3 beam-splitters. The fidelity peaked around \(0.6\) for deterministic approach, and around \(0.77\) for the probabilistic approach (with a 25% chance of error).



  • Homological bosonic code — The Niset-Andersen-Cerf code can be viewed as a scheme to replicate quantum information in multiple regions [3].

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Internal code ID: niset_andersen_cerf

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Zoo Code ID: niset_andersen_cerf

Cite as:
“Niset-Andersen-Cerf code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_niset_andersen_cerf, title={Niset-Andersen-Cerf code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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J. Niset, U. L. Andersen, and N. J. Cerf, “Experimentally Feasible Quantum Erasure-Correcting Code for Continuous Variables”, Physical Review Letters 101, (2008). DOI; 0710.4858
M. Lassen et al., “Quantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code”, Nature Photonics 4, 700 (2010). DOI
P. Hayden et al., “Spacetime replication of continuous variable quantum information”, New Journal of Physics 18, 083043 (2016). DOI; 1601.02544

Cite as:

“Niset-Andersen-Cerf code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.