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

Christian Carisch1 and Oded Zilberberg2

1Institute for Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland.
2Department of Physics, University of Konstanz, 78464 Konstanz, Germany.

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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.

Quantum systems can become far more correlated than their classical counterparts. These correlations, called entanglement, are the key resource for present-day and future quantum technologies. However, it is extremely difficult to quantify entanglement in realistic quantum systems because they tend to correlate with their environment. As a result, the open system shows both classical and quantum correlations. In this work, we are able to separate the classical from quantum correlations when assuming an additional fixed charge symmetry in the system. To this end, we define an easy-to-compute quantity, dubbed the configuration coherence, and prove that it is an entanglement quantifier for a broad range of realistic quantum systems. Finally, we provide an algorithm to efficiently calculate the configuration coherence for one-dimensional systems.

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[3] Gabriele Bellomia, Carlos Mejuto-Zaera, Massimo Capone, and Adriano Amaricci, "Quasilocal entanglement across the Mott-Hubbard transition", Physical Review B 109 11, 115104 (2024).

[4] Cheolhee Han, Yigal Meir, and Eran Sela, "Realistic Protocol to Measure Entanglement at Finite Temperatures", Physical Review Letters 130 13, 136201 (2023).

[5] Lidia Stocker, Stefan H. Sack, Michael S. Ferguson, and Oded Zilberberg, "Entanglement-based observables for quantum impurities", Physical Review Research 4 4, 043177 (2022).

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