Optical implementation of a unitarily correctable code

Abstract

Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum information in a way that is resilient against that noise. Unitarily correctable codes are an error correction technique wherein a single unitary recovery operation is applied without the need for an ancilla Hilbert space. Here, we present the first optical implementation of a nontrivial unitarily correctable code for a noisy quantum channel with no decoherence-free subspaces or noiseless subsystems. We show that recovery of our initial states is achieved with high fidelity (≥ 0.97), quantitatively proving the efficacy of this unitarily correctable code.

Testing Quantum States for Purity

“…We now apply the theory that was developed in to the data sets from the experiments of Schreiter et al. (2009).…”

“…Fig. 1 displays the physical arrangement of the experiments that were performed in Schreiter et al. (2009).…”

“…(2009). In this subsection we give a synopsis of the experiments; a precise scientific description is given in of Schreiter et al. (2009).…”

“…This paper is motivated by the data sets of Schreiter et al. (2009) in experimental demonstration of unitarily correctable codes.…”

Linear-optics realization of channels for single-photon multimode qudits

“…The linear-optics realization of channels has appeared in a number of works for specific cases. For example, random-unitary channels are common in experiments on decoherence-free and unitarily recoverable subspaces [8,9] and in the realization of mixed states [10,11]. The simplest non-trivial example of a channel that is not random-unitary is perhaps given by the qubit amplitude-damping channel [1].…”