Efficient separation of quantum from classical correlations for mixed states with a fixed charge

Entanglement is the key resource for quantum technologies and is at the root of exciting many-body phenomena. How-ever, quantifying the entanglement be-tween two parts of a real-world quan-tum system is challenging when it inter-acts with its environment, as the latter mixes cross-boundary classical with quan-tum correlations. Here, we efficiently quantify quantum correlations in such re-alistic open systems using the operator space entanglement spectrum of a mixed state. If the system possesses a fixed charge, we show that a subset of the spectral values encode coherence between different cross-boundary charge configura-tions. The sum over these values, which we call configuration coherence, can be used as a quantifier for cross-boundary co-herence. Crucially, we prove that for pu-rity non-increasing maps, e.g., Lindblad -type evolutions with Hermitian jump op-erators, the configuration coherence is an entanglement measure. Moreover, it can be efficiently computed using a tensor net-work representation of the state's density matrix. We showcase the configuration co-herence for spinless particles moving on a chain in presence of dephasing. Our approach can quantify coherence and en-tanglement in a broad range of systems and motivates efficient entanglement de-tection.

Automated summary

This article introduces a method for measuring quantum correlations in realistic open systems and proposes a new quantifier. The authors prove the effectiveness of this method in purity non-increasing maps and demonstrate its application in the presence of dephasing in spinless particle chains.