Quantum Correlations beyond Entanglement and Discord

Dissimilar notions of quantum correlations have been established, each being motivated through particular applications in quantum information science and each competing for being recognized as the most relevant measure of quantumness. In this contribution, we experimentally realize a form of quantum correlation that exists even in the absence of entanglement and discord. We certify the presence of such quantum correlations via negativities in the regularized two-mode Glauber-Sudarshan function. Our data show compatibility with an incoherent mixture of orthonormal photon-number states, ruling out quantum coherence and other kinds of quantum resources. By construction, the quantumness of our state is robust against dephasing, thus requiring fewer experimental resources to ensure stability. In addition, we theoretically show how multimode entanglement can be activated based on the generated, nonentangled state. Therefore, we implement a robust kind of nonclassical photon-photon correlated state with useful applications in quantum information processing.

Figure 1

Setup outline. Two single-mode squeezed states are prepared by two OPAs. Combining these beams on a $50:50$ beam splitter with a $\pi /2$ phase shift yields a TMSV state. Introducing a phase randomization (indicated by the phase fluctuation $\delta \phi$) in one of the output arms approximates the desired target state in Eq. (1) [18]. Both final beams are probed by balanced homodyne detectors with controllable phases ${\phi }_{\mathrm{LO},A}$ and ${\phi }_{\mathrm{LO},B}$.

Figure 2

Reconstructed density matrix elements of the TMSV state in photon-number bases, before (top) and after (bottom) phase randomization. Each entry provides the absolute values of the density matrix elements $|{\rho }_{(k,m),(l,n)}|$, where $\widehat{\rho }={\sum }_{k,l,m,n}{\rho }_{(k,m),(l,n)}|k⟩⟨l|\otimes |m⟩⟨n|$. Please note the logarithmic scale. In both plots, $k$ (bottom axis) and $l$ (right axis) denote photon numbers for $A$, and $m$ (left axis) and $n$ (top axis) indicate photon numbers for $B$. Large off-diagonal contributions certify the presence of quantum coherence (top). Strongly diminished off-diagonal elements indicate the absence of quantum coherence (bottom).

Figure 3

Regularized $P$ function sampled from experimental data for the phase-randomized TMSV state, including negativities.