Entanglement catalysis for quantum states and noisy channels

Chandan Datta1,2,3, Tulja Varun Kondra1, Marek Miller1, and Alexander Streltsov1

1Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw, Poland
2Institute for Theoretical Physics III, Heinrich Heine University Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
3Department of Physics, Indian Institute of Technology Jodhpur, Jodhpur 342030, India

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Many applications of the emerging quantum technologies, such as quantum teleportation and quantum key distribution, require singlets, maximally entangled states of two quantum bits. It is thus of utmost importance to develop optimal procedures for establishing singlets between remote parties. As has been shown very recently, singlets can be obtained from other quantum states by using a quantum catalyst, an entangled quantum system which is not changed in the procedure. In this work we take this idea further, investigating properties of entanglement catalysis and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst, which can enable all possible transformations in this setup. We demonstrate the advantage of catalysis in asymptotic settings, going beyond the typical assumption of independent and identically distributed systems. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel when assisted by entangled catalysts. For various types of quantum channels our results lead to optimal protocols, allowing to establish the maximal number of singlets with a single use of the channel.

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Cited by

[1] Chandan Datta, Tulja Varun Kondra, Marek Miller, and Alexander Streltsov, "Catalysis of entanglement and other quantum resources", Reports on Progress in Physics 86 11, 116002 (2023).

[2] Patryk Lipka-Bartosik, Henrik Wilming, and Nelly H. Y. Ng, "Catalysis in Quantum Information Theory", arXiv:2306.00798, (2023).

[3] Ray Ganardi, Tulja Varun Kondra, and Alexander Streltsov, "Catalytic and asymptotic equivalence for quantum entanglement", arXiv:2305.03488, (2023).

[4] I. Henao and R. Uzdin, "Catalytic Leverage of Correlations and Mitigation of Dissipation in Information Erasure", Physical Review Letters 130 2, 020403 (2023).

[5] Elia Zanoni, Thomas Theurer, and Gilad Gour, "Complete Characterization of Entanglement Embezzlement", arXiv:2303.17749, (2023).

[6] Seok Hyung Lie and Hyunseok Jeong, "Delocalized and dynamical catalytic randomness and information flow", Physical Review A 107 4, 042430 (2023).

[7] Chandan Datta, Ray Ganardi, Tulja Varun Kondra, and Alexander Streltsov, "Is There a Finite Complete Set of Monotones in Any Quantum Resource Theory?", Physical Review Letters 130 24, 240204 (2023).

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