Quantum error correction against photon loss using NOON states

Abstract: The so-called NOON states are quantum optical resources known to be useful especially for quantum lithography and metrology. At the same time, they are known to be very sensitive to photon losses and rather hard to produce experimentally. Concerning the former, here we present a scheme where NOON states are the elementary resources for building quantum error correction codes against photon losses, thus demonstrating that such resources can also be useful to suppress the effect of loss. Our NOON-code is an exact code that can be systematically extended from one-photon to higher-number losses. Its loss scaling depending on the codeword photon number is the same as for some existing, exact loss codes such as bosonic and quantum parity codes, but its codeword mode number is intermediate between that of the other codes. Another generalisation of the NOON-code is given for arbitrary logical qudits instead of logical qubits. While, in general, the final codewords are always obtainable from multi-mode NOON states through application of beam splitters, both codewords for the one-photon-loss qubit NOON-code can be simply created from single-photon states with beam splitters. We give various examples and also discuss a potential application of our qudit code for quantum communication.