The noisy Landau-Streater(Werner-Holevo) channel in arbitrary dimensions

• URL: http://arxiv.org/abs/2402.07700v5
• Date: Tue, 6 Aug 2024 16:08:18 GMT
• Title: The noisy Landau-Streater(Werner-Holevo) channel in arbitrary dimensions
• Authors: Vahid Karimipour,
• Abstract summary: Landau-Streater and Werner-Holevo quantum channels are related only in three dimensions, i.e. when acting on qutrits. We show that, in even dimension, this channel has a decomposition in terms of unitary operations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Two important classes of quantum channels, namly the Werner-Holevo and the Landau-Streater channels are known to be related only in three dimensions, i.e. when acting on qutrits. In this work, definition of the Landau-Streater channel is extended in such a way which retains its equivalence to the Werner-Holevo channel in all dimensions. This channel is then modified to be representable as a model of noise acting on qudits. We then investigate propeties of the resulting noisy channel and determine the conditions under which it cannot be the result of a Markovian evolution. Furthermore, we investigate its different capacities for transmitting classical and quantum information with or without entanglement. In particular, while the pure (or high noise) Landau-Streater or the Werner-Holevo channel is entanglement breaking and hence has zero capacity, by finding a lower bound for the quantum capacity, we show that when the level of noise is lower than a critical value the quantum capacity will be non-zero. Surprizingly this value turns out to be approximately equal to $0.4$ in all dimensions. Finally we show that, in even dimension, this channel has a decomposition in terms of unitary operations. This is in contrast with the three dimensional case where it has been proved that such a decomposition is impossible, even in terms of other quantum maps.

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