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Quantum channels and some absolute properties of quantum states

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Abstract

Quantum systems are vulnerable against environmental interactions which may result in depletion of potential resources. The decay in the resources may be to the extent that they cannot be retrieved even with a non-local unitary action on the whole system. Two important figure of merits in the context of quantum information are the fully entangled fraction (FEF) and conditional entropy of a composite quantum system. While FEF plays a key role in teleportation, negativity of conditional entropy assumes significance in state merging and dense coding. A state may lose such merits and may move to an absolute regime, where even a global unitary fails to reclaim those merits. In the present work, we probe the action of some quantum channels in two qubits and two qudits and find that some quantum states move to the absolute regime under the action. Since global unitary operations are unable to retrieve them back to the non-absolute regime, we provide a prescription for the retrieval using an entanglement swap** network. We also provide an explicit illustration of our prescription. Furthermore, we extend the notion of absoluteness to conditional Rényi entropies and find the required condition for a state to have absolute conditional Rényi entropy non-negative property. Exploiting the Bloch-Fano decomposition of density matrices, we characterize such states. We then extend the work to include the marginals of a tripartite system and provide for their characterization with respect to the aforementioned absolute properties.

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Acknowledgements

Tapaswini Patro would like to acknowledge the support from DST-Inspire (INDIA) fellowship No. DST/INSPIRE Fellowship/2019/IF190357. Nirman Ganguly acknowledges support from the project grant received under the SERB(INDIA)-MATRICS scheme vide file number MTR/2022/000101.

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  1. Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, Hyderabad, Telangana, India

    Tapaswini Patro & Nirman Ganguly

  2. Department of Mathematics, Government Girls’ General Degree College, Ekbalpore, Kolkata, India

    Kaushiki Mukherjee

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  1. Tapaswini Patro
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Patro, T., Mukherjee, K. & Ganguly, N. Quantum channels and some absolute properties of quantum states. Quantum Inf Process 23, 228 (2024). https://doi.org/10.1007/s11128-024-04439-1

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