Entangled qubits in a non-Gaussian quantum state

We experimentally generate and tomographically characterize a mixed, genuinely non-Gaussian bipartite continuous-variable entangled state. By testing entanglement in 2$\times$2-dimensional two-qubit subspaces, entangled qubits are localized within the density matrix, which, first, proves the distillability of the state and, second, is useful to estimate the efficiency and test the applicability of distillation protocols. In our example, the entangled qubits are arranged in the density matrix in an asymmetric way, i.e., entanglement is found between diverse qubits composed of different photon number states, although the entangled state is symmetric under exchanging the modes.

Figure 1

Simplified sketch of the experimental setup. LO: local oscillator; OPA: optical parametric amplifier (squeezed light source); BHD: balanced homodyne detector; PZT: piezoelectrically actuated mirror applying the phase noise. Aux: Frequency shifted weak field providing a readout for the difference of the detection phases of BHDa and BHDb.

Figure 2

Reconstructed two-mode density matrix of the examined entangled state in the Fock basis. A block $\mathit{mn}$ provides the absolute values of the density matrix elements ${\rho }_{\mathit{kl},\mathit{mn}}$, where $k,l$ refers to the photon numbers at BHDa, and $m,n$ to those at BHDb.

Figure 3

Probabilities for the occurrence of entangled two-qubit subspaces. The statistical significance of the successful entanglement tests is color coded. It represents the smallest (negative) eigenvalue of the partially transposed state in units of the corresponding standard deviation $\sigma$.

Figure 4

Probability of finding a singlet state $|{\psi }^{-}\rangle$ in a specific qubit subsystem.