Quantum correlation provides a promising measure beyond entanglement. Here, we propose a necessary and sufficient condition for nonzero quantum correlation in continuous variable systems, which is simple and easy to perform in terms of a marker Q r . In order to get this condition, we introduce continuous-variable local orthogonal bases of the operator space, which are generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we obtain the marker Q r for all bipartite continuous variable states, and provide several examples including two-mode Gaussian and non-Gaussian states. Our result may provide a candidate for quantum correlation measures, and can be measured by designed quantum circuits.Quantum correlation provides a promising measure beyond entanglement. Here, we propose a necessary and sufficient condition for nonzero quantum correlation in continuous variable systems, which is simple and easy to perform in terms of a marker Q r . In order to get this condition, we introduce continuous-variable local orthogonal bases of the operator space, which are generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we obtain the marker Q r for all bipartite continuous variable states, and provide several examples including two-mode Gaussian and non-Gaussian states. Our result may provide a candidate for quantum correlation measures, and can be measured by designed quantum circuits.

arXiv:1308.4810New Journal of PhysicsSep 10, 20151 citation

Quantum correlations for bipartite continuous-variable systems

Ruifen Ma, Jinchuan Hou, Xiaofei Qi +1 more

Quantum Information ProcessingMar 8, 20186 citations

Genuine Hybrid Number-Polarization Entanglement

Dorian Schiffer, Marcus Huber, Elizabeth Agudelo

Entanglement is a key resource for fundamental tests of physics and emerging quantum technologies. In quantum optics, two perspectives on entanglement coexist. In the continuous-variable framework, entanglement is understood as holding between optical modes. In contrast, discrete-variable quantum optics focuses on quantum correlations in degrees of freedom such as polarization that label fixed numbers of photons. In this paper, we show that entanglement can transcend this separation. Spontaneous parametric down-conversion inherently generates correlations in optical phase space, photon number, and labelling degrees of freedom simultaneously. In polarization, this structure is traditionally described by macroscopic Bell states. Existing witnesses, however, fail to detect the genuine hybrid entanglement of these states, which goes beyond the continuous-discrete-variable categorization. Here, we lay the groundwork for a general framework unifying continuous- and discrete-variable notions of entanglement. In particular, we derive an operational witness providing a sufficient criterion for genuine hybrid number-polarization entanglement and outline its experimental implementation. Finally, we discuss exemplary states which, together with our results on macroscopic Bell states, motivate a broader classification of genuine hybrid quantum correlations.Entanglement is a key resource for fundamental tests of physics and emerging quantum technologies. In quantum optics, two perspectives on entanglement coexist. In the continuous-variable framework, entanglement is understood as holding between optical modes. In contrast, discrete-variable quantum optics focuses on quantum correlations in degrees of freedom such as polarization that label fixed numbers of photons. In this paper, we show that entanglement can transcend this separation. Spontaneous parametric down-conversion inherently generates correlations in optical phase space, photon number, and labelling degrees of freedom simultaneously. In polarization, this structure is traditionally described by macroscopic Bell states. Existing witnesses, however, fail to detect the genuine hybrid entanglement of these states, which goes beyond the continuous-discrete-variable categorization. Here, we lay the groundwork for a general framework unifying continuous- and discrete-variable notions of entanglement. In particular, we derive an operational witness providing a sufficient criterion for genuine hybrid number-polarization entanglement and outline its experimental implementation. Finally, we discuss exemplary states which, together with our results on macroscopic Bell states, motivate a broader classification of genuine hybrid quantum correlations.

quant-pharXiv:2605.26962May 27, 20260 citations

Necessary and sufficient condition for nonzero quantum discord in continuous variable systems

Chengjie Zhang, Sixia Yu, Qing Chen +2 more

Quantum discord provides a promising measure for the quantum correlation beyond entanglement, and may be responsible for the quantum speedup in certain quantum computing tasks. Here, we propose a necessary and sufficient condition for nonzero quantum discord in continuous variable systems, which is simple and easy to perform in terms of a marker $Q$ . In order to obtain this condition, we introduce the continuous-variable local orthogonal basis of the operator space generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we derive an explicit expression of the marker $Q$ for all the two-mode states, and present examples of all Gaussian states and several non-Gaussian states. Our result provides a candidate for quantum correlation measures, and can be easily measured by a designed quantum circuit.Quantum discord provides a promising measure for the quantum correlation beyond entanglement, and may be responsible for the quantum speedup in certain quantum computing tasks. Here, we propose a necessary and sufficient condition for nonzero quantum discord in continuous variable systems, which is simple and easy to perform in terms of a marker $Q$. In order to obtain this condition, we introduce the continuous-variable local orthogonal basis of the operator space generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we derive an explicit expression of the marker $Q$ for all the two-mode states, and present examples of all Gaussian states and several non-Gaussian states. Our result provides a candidate for quantum correlation measures, and can be easily measured by a designed quantum circuit.

Aug 22, 20130 citations

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. In order to obtain this condition, we introduce the continuous-variable local orthogonal basis of the operator space generalized from the orthogonal basis sets in local operator space for discrete variables. Based on this, we derive an explicit expression of the marker

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for all the two-mode states, and present examples of all Gaussian states and several non-Gaussian states. Our result provides a candidate for quantum correlation measures, and can be easily measured by a designed quantum circuit.