Quantum coherences of indistinguishable particles

We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this concept to the many-particle scenario and determine the influence of the exchange symmetry. Moreover, we characterize the relation of multiparticle coherence to the entanglement of the compound quantum system. To support our general treatment with examples, we consider the quantum correlations of a collection of qudits. The impact of local and global quantum superpositions on the different forms of quantum correlations is discussed. For differently correlated states in the bipartite and multipartite scenarios, we provide a comprehensive characterization of the various forms and origins of quantum correlations.

Figure 1

The interplay of different origins of multiparticle quantum correlations is schematically outlined in (a). The considered types of particles together with the underlying tensor products and the signs used for their identification are listed in (b).

Figure 2

The expectation value of the test operator $L=|\chi \rangle \langle \chi |$ [Eq. (35)] for the state ${\varrho }_{\mathrm{\Delta }\phi }$ [Eq. (37)] is shown as a function of the dephasing parameter $\mathrm{\Delta }\phi$ and for $\kappa =1/2$. The maximal expectation values for the different forms of classical states [Eq. (36)] are depicted as horizontal dashed and dot-dashed lines. For all $\mathrm{\Delta }\phi <\pi$, we verify quantum coherence for the distinguishable and indistinguishable cases as well as for entanglement based on $\otimes$. Bosonic entanglement, using $\vee$, is detected for a dephasing less than the bound which is indicated by the vertical dotted line.