Density Matrix: Entangled States

Sergey N. Filippov, Vladimir I. Man’ko

Yong Heng Zhou

We point out that density matrices can only be used to describe quantum states, so the entanglement contained in a density matrix is just quantum entanglement. This means a bipartite state described by a density matrix contains quantum entanglement, unless the density matrix has the form $ρ_{AB}=ρ_A\otimes ρ_B$.

Yusuke Masaki, Takashi Otaki, Hiroaki Matsueda

Quantum entanglement is one of the most intriguing features of quantum mechanics. To investigate the entanglement between two excitons in a biexciton, an experimental technique called density matrix spectroscopy (DMS) has recently been developed. DMS combines stimulated emission tomography and pump-probe techniques to obtain a time-resolved density matrix of the polarization state of a photon pair emitted from the biexciton. The reconstructed density matrix is expected to encode information about the biexciton state and its entanglement dynamics, but the precise nature of this connection has remained unclear. In this paper, we derive an analytical relationship between the density matrix obtained by DMS and the biexciton state. In addition, we perform numerical simulations to compare the entanglement dynamics obtained by DMS with the biexciton's entanglement dynamics in a two-dimensional electron-hole system using an extended ionic Hubbard model. We find that DMS can partially capture the entanglement in the biexciton, in particular, the dynamics of the difference $S_{\mathrm{bi}} - S_k$, where $S_{\mathrm{bi}}$ is the entanglement entropy of the biexciton and $S_k$ is the entanglement in terms of the wavevectors of the excitons that constitute the biexciton. These results demonstrate the validity of DMS for obtaining information about the entanglement dynamics of the biexciton.

Qin Guo

A density matrix is usually obtained by solving the Bloch equation, however only a few Hamiltonians' density matrices can be analytically derived. The density matrix for two interacting particles with kinetic coupling is hard to derive by the usual method due to this coupling; this paper solves this problem by using the bipartite entangled state representation.