Abstract
Abstract We design a scheme for detecting a single photon loss from multi-modal quantum signals transmitted via a fiber or in free space. This consists of a special type of unitary coding transformation, the parity controlled-squeezing, applied prior to the transmission on the signal composed by information and ancilla modes. At the receiver, the inverse unitary transformation is applied—decoding, and the ancilla mode is measured via photon detection. The outcome reveals whether a photon loss has occurred. Distortion of the information part of the signal caused by an ancilla photon loss can be corrected via unitary transformation while loss of a photon from the information part of the signal can be detected with the probability exponentially close to unity but cannot be corrected. In contrast to the schemes of decoherence free subspaces and quantum error correction protocols, this method allows one to make use in principle of entire Hilbert space dimensionality. We discuss possible ways of synthesizing the required encoding–decoding transformation.