# Optimal probabilistic cloning of two linearly independent states with arbitrary probability distribution

Optimal probabilistic cloning of two linearly independent states with arbitrary probability... We investigate the probabilistic quantum cloning (PQC) of two states with arbitrary probability distribution. The optimal success probabilities are worked out for $$1\rightarrow 2$$ 1 → 2 PQC of the two states. The results show that the upper bound on the success probabilities of PQC in Qiu (J Phys A 35:6931–6937, 2002) cannot be reached in general. With the optimal success probabilities, we design simple forms of $$1\rightarrow 2$$ 1 → 2 PQC and work out the unitary transformation needed in the PQC processes. The optimal success probabilities for $$1\rightarrow 2$$ 1 → 2 PQC are also generalized to the $$M\rightarrow N$$ M → N PQC case. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Optimal probabilistic cloning of two linearly independent states with arbitrary probability distribution

Quantum Information Processing, Volume 15 (2) – Dec 10, 2015
11 pages

/lp/springer_journal/optimal-probabilistic-cloning-of-two-linearly-independent-states-with-8EWt7XAgwX
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/s11128-015-1170-2
Publisher site
See Article on Publisher Site

### Abstract

We investigate the probabilistic quantum cloning (PQC) of two states with arbitrary probability distribution. The optimal success probabilities are worked out for $$1\rightarrow 2$$ 1 → 2 PQC of the two states. The results show that the upper bound on the success probabilities of PQC in Qiu (J Phys A 35:6931–6937, 2002) cannot be reached in general. With the optimal success probabilities, we design simple forms of $$1\rightarrow 2$$ 1 → 2 PQC and work out the unitary transformation needed in the PQC processes. The optimal success probabilities for $$1\rightarrow 2$$ 1 → 2 PQC are also generalized to the $$M\rightarrow N$$ M → N PQC case.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 10, 2015

### References

• Probabilistic cloning with supplementary information contained in the quantum states of two auxiliary systems
Li, L; Qiu, DW
• Probabilistic cloning of three nonorthogonal states
Zhang, W; Rui, P; Yang, Q; Zhao, Y; Zhang, Z
• A probabilistic cloning machine for replicating two non-orthogonal states
Duan, LM; Guo, GC
• Local cloning of multipartite entangled states

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