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International Conference on Quantum Information

Qubits, Qutrits and Gaussian states in Noisy Quantum Channels

Krzysztof Wódkiewicz

Published Jan 1, 2007• 0 citations
Publisher

Abstract

Entanglement for qubits, qutrits and Gaussian states in quantum channels is investigated. The channels involve stochastic noise with zero-bandwidth or spontaneous emission. Exact results concerning entanglement of Werner states in such channels are presented.
DOI
10.1364/icqi.2007.ifa1

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Two important classes of quantum channels, namely, 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 that it 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 properties 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 nonzero. Surprisingly, 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 impossible, even in terms of other quantum maps.
A simple model describing depolarization channels with zero-bandwidth environment is presented and exactly solved. The environment is modeled by Lorentzian, telegraphic, and Gaussian zero-bandwidth noises. Such channels can go beyond the standard Markov dynamics and therefore can illustrate the influence of memory effects of the noisy communication channel on the transmitted information. To quantify the disturbance of quantum states the entanglement fidelity between arbitrary input and output states is investigated.
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 0.40.40.4 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.