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.

DOI: 10.1103/physreva.72.032335

Related papers

Probabilistic cloning with supplementary information

Koji Azuma, Junichi Shimamura, Masato Koashi +1 more

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 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.

Conference on Lasers and Electro-OpticsJan 1, 20053 citations

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.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.

arXiv:quant-ph/0511058Journal of Physics A Mathematical and GeneralApr 19, 200616 citations

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

Daowen Qiu

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 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.

Nov 7, 20050 citations

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.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/0204153Apr 26, 200214 citations

Assisted cloning and orthogonal complementing of an unknown state

Arun Kumar Pati

We propose a protocol where one can exploit dual quantum and classical channels to achieve perfect ``cloning'' and ``orthogonal-complementing'' of an unknown state with minimal assistance from a state preparer (without revealing what the input state is). The first stage of the protocol requires usual teleportation, and in the second stage the preparer disentangles the leftover entangled states by a single-particle measurement process and communicates a number of classical bits (1-cbit per copy) to different parties so that perfect copies and complement copies are produced. Our protocol produces clones and complement clones of unknown qubit each with a probability $\frac{1}{2}$ and clones of real qubit with unit probability.We propose a protocol where one can exploit dual quantum and classical channels to achieve perfect ``cloning'' and ``orthogonal-complementing'' of an unknown state with minimal assistance from a state preparer (without revealing what the input state is). The first stage of the protocol requires usual teleportation, and in the second stage the preparer disentangles the leftover entangled states by a single-particle measurement process and communicates a number of classical bits (1-cbit per copy) to different parties so that perfect copies and complement copies are produced. Our protocol produces clones and complement clones of unknown qubit each with a probability $\frac{1}{2}$ and clones of real qubit with unit probability.

arXiv:quant-ph/9904068Physical Review AJan 14, 200091 citations

Optimal copy complexity of quantum state cloning

Sangwoo Jeon, Vaughn Sohn, Changhun Oh

Quantum state cloning is the task of approximately producing additional copies of an unknown quantum state from a finite number of input copies. The optimal cloning fidelity is known exactly for pure states, but no comparable characterization is known for general mixed states. We determine the optimal asymptotic copy complexity for $d$ -dimensional states of rank at most $r$ : producing $M$ additional copies with worst-case fidelity at least $1-\varepsilon$ requires and is achievable with $N=Θ(Mrd/\varepsilon)$ input copies. Remarkably, the lower bound already holds for a family of states with a fixed flat spectrum, while the matching upper bound is achieved by random purification followed by optimal pure-state cloning. For $M=1$ , we further show that high-fidelity tomography can be coherently converted into cloning with comparable error, revealing an operational origin of the matching cloning and tomography complexities.Quantum state cloning is the task of approximately producing additional copies of an unknown quantum state from a finite number of input copies. The optimal cloning fidelity is known exactly for pure states, but no comparable characterization is known for general mixed states. We determine the optimal asymptotic copy complexity for $d$-dimensional states of rank at most $r$: producing $M$ additional copies with worst-case fidelity at least $1-\varepsilon$ requires and is achievable with $N=Θ(Mrd/\varepsilon)$ input copies. Remarkably, the lower bound already holds for a family of states with a fixed flat spectrum, while the matching upper bound is achieved by random purification followed by optimal pure-state cloning. For $M=1$, we further show that high-fidelity tomography can be coherently converted into cloning with comparable error, revealing an operational origin of the matching cloning and tomography complexities.

quant-pharXiv:2608.24484Aug 26, 20260 citations

m

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

m

\frac{1}{2}

and clones of real qubit with unit probability.

d

-dimensional states of rank at most

r

: producing

M

additional copies with worst-case fidelity at least

1-\varepsilon

requires and is achievable with

N=Θ(Mrd/\varepsilon)

input copies. Remarkably, the lower bound already holds for a family of states with a fixed flat spectrum, while the matching upper bound is achieved by random purification followed by optimal pure-state cloning. For

M=1

, we further show that high-fidelity tomography can be coherently converted into cloning with comparable error, revealing an operational origin of the matching cloning and tomography complexities.