The noisy Landau-Streater(Werner-Holevo) channel in arbitrary dimensions
- URL: http://arxiv.org/abs/2402.07700v4
- Date: Thu, 7 Mar 2024 04:17:16 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 dimensions, 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, the 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
dimensions, 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 possible is impossible, even in terms of other
quantum maps.
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