We study the probabilistic cloning of three symmetric states. These states are defined by a single complex quantity, the inner product among them. We show that three different probabilistic cloning machines are necessary to optimally clone all possible families of three symmetric states. We also show that the optimal cloning probability of generating $M$ copies out of one original can be cast as the quotient between the success probability of unambiguously discriminating one and $M$ copies of symmetric states.We study the probabilistic cloning of three symmetric states. These states are defined by a single complex quantity, the inner product among them. We show that three different probabilistic cloning machines are necessary to optimally clone all possible families of three symmetric states. We also show that the optimal cloning probability of generating $M$ copies out of one original can be cast as the quotient between the success probability of unambiguously discriminating one and $M$ copies of symmetric states.

Physical Review ADec 10, 201020 citations

Probabilistic quantum cloning of three symmetric states

Shouya Wang, Wen‐Hai Zhang

This paper investigates the 1 → M probabilistic quantum cloning of three symmetric states, which are defined by a complex number of their inner product. First, a general transformation of the 1 → M probabilistic quantum cloning is designed, and the ancillary success states are introduced. Then, the explicit expression of the probability of successful cloning is derived, which depends on the number M and the inner product of the three symmetric states. Finally, three examples are provided to demonstrate the efficiency of our cloning transformation.This paper investigates the 1 → M probabilistic quantum cloning of three symmetric states, which are defined by a complex number of their inner product. First, a general transformation of the 1 → M probabilistic quantum cloning is designed, and the ancillary success states are introduced. Then, the explicit expression of the probability of successful cloning is derived, which depends on the number M and the inner product of the three symmetric states. Finally, three examples are provided to demonstrate the efficiency of our cloning transformation.

AIP AdvancesDec 1, 20240 citations

Probabilistic cloning of three nonorthogonal states

Wen Zhang, Pinshu Rui, Qun Yang +2 more

Quantum Information ProcessingJan 28, 20156 citations

Probabilistic cloning of equidistant states

O. Jiménez, Luis Roa, A. Delgado

We study the probabilistic cloning of equidistant states. These states are such that the inner product between them is a complex constant or its conjugate. Thereby, it is possible to study their cloning in a simple way. In particular, we are interested in the behavior of the cloning probability as a function of the phase of the overlap among the involved states. We show that for certain families of equidistant states Duan and Guo's cloning machine leads to cloning probabilities lower than the optimal unambiguous discrimination probability of equidistant states. We propose an alternative cloning machine whose cloning probability is higher than or equal to the optimal unambiguous discrimination probability for any family of equidistant states. Both machines achieve the same probability for equidistant states whose inner product is a positive real number.We study the probabilistic cloning of equidistant states. These states are such that the inner product between them is a complex constant or its conjugate. Thereby, it is possible to study their cloning in a simple way. In particular, we are interested in the behavior of the cloning probability as a function of the phase of the overlap among the involved states. We show that for certain families of equidistant states Duan and Guo's cloning machine leads to cloning probabilities lower than the optimal unambiguous discrimination probability of equidistant states. We propose an alternative cloning machine whose cloning probability is higher than or equal to the optimal unambiguous discrimination probability for any family of equidistant states. Both machines achieve the same probability for equidistant states whose inner product is a positive real number.

Physical Review AAug 25, 201023 citations

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copies out of one original can be cast as the quotient between the success probability of unambiguously discriminating one and

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copies of symmetric states.