# Probabilistic cloning of three nonorthogonal states

Probabilistic cloning of three nonorthogonal states We study the probabilistic cloning of three nonorthogonal states with equal success probabilities. For simplicity, we assume that the three states belong to a special set. Analytical form of the maximal success probability for $$M\rightarrow N$$ M → N probabilistic cloning is calculated. With the maximal success probability, we deduce the explicit form of $$M\rightarrow N$$ M → N probabilistic quantum cloning machine. In the case of $$1\rightarrow 2$$ 1 → 2 cloning, we get the unambiguous form of the unitary operation. It is demonstrated that the upper bound for probabilistic quantum cloning machine in (Qiu in J Phys A 35:6931, 2002) can be reached only if the three states are equidistant. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Probabilistic cloning of three nonorthogonal states

, Volume 14 (4) – Jan 29, 2015
12 pages

/lp/springer_journal/probabilistic-cloning-of-three-nonorthogonal-states-VGyT571wcs
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-0921-4
Publisher site
See Article on Publisher Site

### Abstract

We study the probabilistic cloning of three nonorthogonal states with equal success probabilities. For simplicity, we assume that the three states belong to a special set. Analytical form of the maximal success probability for $$M\rightarrow N$$ M → N probabilistic cloning is calculated. With the maximal success probability, we deduce the explicit form of $$M\rightarrow N$$ M → N probabilistic quantum cloning machine. In the case of $$1\rightarrow 2$$ 1 → 2 cloning, we get the unambiguous form of the unitary operation. It is demonstrated that the upper bound for probabilistic quantum cloning machine in (Qiu in J Phys A 35:6931, 2002) can be reached only if the three states are equidistant.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 29, 2015

### References

• Probabilistic cloning with supplementary information contained in the quantum states of two auxiliary systems
Li, L; Qiu, DW
• A probabilistic cloning machine for replicating two non-orthogonal states
Duan, LM; Guo, GC
• Local cloning of multipartite entangled states

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