Immunity of information encoded in decoherence-free subspaces to particle loss

We demonstrate that for an ensemble of qudits, subjected to collective decoherence in the form of perfectly correlated random SU($d$) unitaries, quantum superpositions stored in the decoherence-free subspace are fully immune against the removal of one particle. This provides a feasible scheme to protect quantum information encoded in the polarization state of a sequence of photons against both collective depolarization and one-photon loss and can be demonstrated with photon quadruplets using currently available technology.

Figure 1

Diagrams depicting three nonequivalent products of two-qubit singlet states defined in Eq. (4). The qubits are represented as dots with connections identifying pairs that form singlet states.

Figure 2

An experimental scheme for loss-tolerant detection of a logical qubit encoded in four photons. The projection basis $|{\Xi }_k\rangle$, $|{\Xi }_k^{\perp }\rangle$, where $k=1,2,3$, is selected by a suitable rerouting of input photons. Pairs of photons are interfered on two balanced beam splitters and photon numbers are counted at their outputs. Combinations of outcomes for individual detectors that correspond to unambiguous identification of $|{\Xi }_k\rangle$ and $|{\Xi }_k^{\perp }\rangle$ are indicated with photon numbers in curly brackets. The ordering within both inner and outer brackets does not matter.