Pati, Arun K. (2003) Geometric phases for mixed states during unitary and non-unitary evolutions International Journal of Quantum Information, 01 (01). pp. 135-152. ISSN 0219-7499
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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S02...
Related URL: http://dx.doi.org/10.1142/S0219749903000103
Abstract
Mixed states typically arise when quantum systems interact with the outside world. Evolution of open quantum systems in general are described by quantum operations which are represented by completely positive maps. We elucidate the notion of geometric phase for a quantum system described by a mixed state undergoing unitary evolution and non-unitary evolutions. We discuss parallel transport condition for mixed states both in the case of unitary maps and completely positive maps. We find that the relative phase shift of a system not only depends on the state of the system, but also depends on the initial state of the ancilla with which it might have interacted in the past. The geometric phase change during a sequence of quantum operations is shown to be non-additive in nature. This property can attribute a "memory" to a quantum channel. We explore these ideas and illustrate them with simple examples.
Item Type: | Article |
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Source: | Copyright of this article belongs to World Scientific Publishing Company. |
ID Code: | 105441 |
Deposited On: | 09 Mar 2018 11:41 |
Last Modified: | 09 Mar 2018 11:41 |
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