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Novel cloning machine with supplementary information for copying quantum superposition of multiple clones

Daowen Qiu

Published Nov 7, 2005• 0 citations
OpenAlex

Abstract

Probabilistic cloning was first proposed by Duan and Guo. Then Pati established a novel cloning machine (NCM) for copying quantum superposition of multiple clones. In this paper, we deal with the novel cloning machine with supplementary information (NCMSI) for obtaining quantum superposition of multiple clones. For the case of cloning two states, we demonstrate that the optimal efficiency of the NCMSI in which the original party and the supplementary party can perform quantum communication equals that achieved by a two-step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties. From this equivalence it follows that NCMSI may increase the success probabilities for copying. Also, an upper bound on the unambiguous discrimination of two nonorthogonal pure produce states is derived. Our investigation generalizes and completes the result in the literature.

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Novel cloning machine with supplementary information

Daowen Qiu

Probabilistic cloning was first proposed by Duan and Guo. Then Pati established a novel cloning machine (NCM) for copying superposition of multiple clones simultaneously. In this paper, we deal with the novel cloning machine with supplementary information (NCMSI). For the case of cloning two states, we demonstrate that the optimal efficiency of the NCMSI in which the original party and the supplementary party can perform quantum communication equals that achieved by a two-step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties. From this equivalence, it follows that NCMSI may increase the success probabilities for copying. Also, an upper bound on the unambiguous discrimination of two nonorthogonal pure product states is derived. Our investigation generalizes and completes the results in the literature.

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A stronger no-cloning theorem

Richard Jozsa

It is well known that (non-orthogonal) pure states cannot be cloned so one may ask: how much or what kind of additional (quantum) information is needed to supplement one copy of a quantum state in order to be able to produce two copies of that state by a physical operation? For classical information, no supplementary information is required. However for pure quantum (non-orthogonal) states, we show that the supplementary information must always be as large as it can possibly be i.e. the clone must be able to be generated from the additional information alone, independently of the first (given) copy.

arXiv:quant-ph/0204153•Apr 26, 2002•14 citations
Probabilistic cloning was first proposed by Duan and Guo. Then Pati established a novel cloning machine (NCM) for copying quantum superposition of multiple clones. In this paper, we deal with the novel cloning machine with supplementary information (NCMSI) for obtaining quantum superposition of multiple clones. For the case of cloning two states, we demonstrate that the optimal efficiency of the NCMSI in which the original party and the supplementary party can perform quantum communication equals that achieved by a two-step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties. From this equivalence it follows that NCMSI may increase the success probabilities for copying. Also, an upper bound on the unambiguous discrimination of two nonorthogonal pure produce states is derived. Our investigation generalizes and completes the result in the literature.
Probabilistic cloning was first proposed by Duan and Guo. Then Pati established a novel cloning machine (NCM) for copying superposition of multiple clones simultaneously. In this paper, we deal with the novel cloning machine with supplementary information (NCMSI). For the case of cloning two states, we demonstrate that the optimal efficiency of the NCMSI in which the original party and the supplementary party can perform quantum communication equals that achieved by a two-step cloning protocol wherein classical communication is only allowed between the original and the supplementary parties. From this equivalence, it follows that NCMSI may increase the success probabilities for copying. Also, an upper bound on the unambiguous discrimination of two nonorthogonal pure product states is derived. Our investigation generalizes and completes the results in the literature.
We consider probabilistic cloning of a state chosen from a mutually nonorthogonal set of pure states, with the help of a party holding supplementary information in the form of pure states. When the number of states is 2, we show that the best efficiency of producing mmm copies is always achieved by a two-step protocol in which the helping party first attempts to produce $m\ensuremath{-}1$ copies from the supplementary state, and if it fails, then the original state is used to produce mmm copies. On the other hand, when the number of states exceeds two, the best efficiency is not always achieved by such a protocol. We give examples in which the best efficiency is not achieved even if we allow any amount of one-way classical communication from the helping party.
We consider probabilistic cloning of a state chosen from a mutually nonorthogonal set of pure states, with the help of a party holding supplementary information in the form of pure states. When the number of states is two, we show that the best efficiency of producing m copies is always achieved by a two-step protocol in which the helping party first attempts to produce m-1 copies from the supplementary state, and if it fails, then the original state is used to produce m copies. On the other hand, when the number of states exceeds two, the best efficiency is not always achieved by such a protocol. We give examples in which the best efficiency is not achieved even if we allow any amount of one-way classical communication from the helping party.
We envisage a novel quantum cloning machine, which takes an input state and produces an output state whose success branch can exist in a linear superposition of multiple copies of the input state and the failure branch can exist in a superposition of composite states independent of the input state. We prove that unknown nonorthogonal states chosen from a set SSS can evolve into a linear superposition of multiple clones and failure branches by a unitary process if and only if the states are linearly independent. We derive a bound on the success probability of the novel cloning machine. We argue that the deterministic and probabilistic clonings are special cases of our novel cloning machine.
The method of quantum cloning is divided into two main categories: approximate and probabilistic quantum cloning. The former method is used to approximate an unknown quantum state deterministically, and the latter can be used to faithfully copy the state probabilistically. Thus far, many approximate cloning machines have been experimentally demonstrated, but probabilistic cloning remains an experimental challenge, as it requires more complicated networks and a higher level of precision control. In this work, we design an efficient quantum network with a limited amount of resources and perform the first experimental demonstration of probabilistic quantum cloning in a NMR quantum computer. In our experiment, the optimal cloning efficiency proposed by Duan and Guo [Phys. Rev. Lett. 80, 4999 (1998)] is achieved.
It is well known that (non-orthogonal) pure states cannot be cloned so one may ask: how much or what kind of additional (quantum) information is needed to supplement one copy of a quantum state in order to be able to produce two copies of that state by a physical operation? For classical information, no supplementary information is required. However for pure quantum (non-orthogonal) states, we show that the supplementary information must always be as large as it can possibly be i.e. the clone must be able to be generated from the additional information alone, independently of the first (given) copy.