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

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2023
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Carisch, Christian
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Quantum. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. 2023, 7, 954. eISSN 2521-327X. Available under: doi: 10.22331/q-2023-03-20-954
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Entanglement is the key resource for quantum technologies and is at the root of exciting many-body phenomena. However, quantifying the entanglement between two parts of a real-world quantum system is challenging when it interacts with its environment, as the latter mixes cross-boundary classical with quantum correlations. Here, we efficiently quantify quantum correlations in such realistic 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 configurations. The sum over these values, which we call "configuration coherence", can be used as a quantifier for cross-boundary coherence. Crucially, we prove that for purity non-increasing maps, e.g., Lindblad-type evolutions with Hermitian jump operators, the configuration coherence is an entanglement measure. Moreover, it can be efficiently computed using a tensor network representation of the state's density matrix. We showcase the configuration coherence for spinless particles moving on a chain in presence of dephasing. Our approach can quantify coherence and entanglement in a broad range of systems and motivates efficient entanglement detection.

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ISO 690CARISCH, Christian, Oded ZILBERBERG, 2023. Efficient separation of quantum from classical correlations for mixed states with a fixed charge. In: Quantum. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. 2023, 7, 954. eISSN 2521-327X. Available under: doi: 10.22331/q-2023-03-20-954
BibTex
@article{Carisch2023Effic-66736,
  year={2023},
  doi={10.22331/q-2023-03-20-954},
  title={Efficient separation of quantum from classical correlations for mixed states with a fixed charge},
  volume={7},
  journal={Quantum},
  author={Carisch, Christian and Zilberberg, Oded},
  note={Article Number: 954}
}
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