Geometrical conditions for completely positive trace-preserving maps and their application to a quantum repeater and a state-dependent quantum cloning machine
- Imai Quantum Computing and Information Project, Bunkyo-ku, Tokyo 113-0033 (Japan)
- Communications Research Laboratory, Koganei, Tokyo 184-8795 (Japan)
We address the problem of finding optimal CPTP (completely positive trace-preserving) maps between a set of binary pure states and another set of binary generic mixed state in a two-dimensional space. The necessary and sufficient conditions for the existence of such CPTP maps can be discussed within a simple geometrical picture. We exploit this analysis to show the existence of an optimal quantum repeater which is superior to the known repeating strategies for a set of coherent states sent through a lossy quantum channel. We also show that the geometrical formulation of the CPTP mapping conditions can be a simpler method to derive a state-dependent quantum (anti) cloning machine than the study so far based on the explicit solution of several constraints imposed by unitarity in an extended Hilbert space.
- OSTI ID:
- 20640314
- Journal Information:
- Physical Review. A, Vol. 68, Issue 4; Other Information: DOI: 10.1103/PhysRevA.68.042327; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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