International Journal of Quantum Information

Analytical expression of the geometric quantum discord generated by asymmetric cloning

Irina Ion, Iulia Ghiu

Published Dec 30, 2025• 0 citations

Abstract

We analyze the output mixed states generated when the asymmetric cloners are applied on a pure two-qubit state. We investigate two kinds of cloners: (a) local [Formula: see text] optimal universal asymmetric cloning machines and (b) nonlocal [Formula: see text] optimal universal asymmetric cloning machines. In both cases we find analytical formulae of the geometric quantum discord of the two clones. Finally, we prove that the geometric quantum discord generated by the nonlocal asymmetric cloners is not smaller than the geometric quantum discord given by the local asymmetric cloners.

DOI: 10.1142/s0219749925400131

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International Journal of Quantum Information

Analytical expression of the geometric quantum discord generated by asymmetric cloning

Irina Ion, Iulia Ghiu

Published Dec 30, 2025• 0 citations

Publisher

Abstract

DOI: 10.1142/s0219749925400131

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Analysis of Quantum Correlations Obtained Using Local Optimal Universal Asymmetric Cloners

Cătălina Cîrneci, Iulia Ghiu

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Asymmetric cloning of steering, quantum discord, and coherence

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We investigate the optimal distribution of quantum information over multipartite systems in asymmetric settings. We introduce cloning transformations that take $N$ identical replicas of a pure state in any dimension as input and yield a collection of clones with nonidentical fidelities. As an example, if the clones are partitioned into a set of ${M}_{A}$ clones with fidelity ${F}^{A}$ and another set of ${M}_{B}$ clones with fidelity ${F}^{B}$ , the trade-off between these fidelities is analyzed, and particular cases of optimal $N\ensuremath{\rightarrow}{M}_{A}+{M}_{B}$ cloning machines are exhibited. We also present an optimal $1\ensuremath{\rightarrow}1+1+1$ cloning machine, which is an example of a tripartite fully asymmetric cloner. Finally, it is shown how these cloning machines can be optically realized.We investigate the optimal distribution of quantum information over multipartite systems in asymmetric settings. We introduce cloning transformations that take $N$ identical replicas of a pure state in any dimension as input and yield a collection of clones with nonidentical fidelities. As an example, if the clones are partitioned into a set of ${M}_{A}$ clones with fidelity ${F}^{A}$ and another set of ${M}_{B}$ clones with fidelity ${F}^{B}$, the trade-off between these fidelities is analyzed, and particular cases of optimal $N\ensuremath{\rightarrow}{M}_{A}+{M}_{B}$ cloning machines are exhibited. We also present an optimal $1\ensuremath{\rightarrow}1+1+1$ cloning machine, which is an example of a tripartite fully asymmetric cloner. Finally, it is shown how these cloning machines can be optically realized.

arXiv:quant-ph/0411179Physical Review AOct 26, 200570 citations

In this work, we exhaustively investigate

1 \rightarrow 2

local and non local broadcasting of entanglement and correlations (optimal and non-optimal) using asymmetric Pauli cloners, with the most general two qubit state as a resource. We exemplify the broadcasting of entanglement using Maximally Entangled Mixed States and demostrate the variation of broadcasting range with the amount of entanglement in resource state as well as the asymmetry in the cloner. We show that it is impossible to optimally broadcast quantum correlations that go beyond entanglement (Geometric Discord) with the help of these asymmetric Pauli cloning machines. We introduce the concept of asymmetry in correlations to quantify the degree of variation in the amount of correlation present in the output pairs obtained after broadcasting. We also study the problem of

1 \rightarrow 3

broadcasting of entanglement using non-maximally entangled state (NME) as a resource. We adopt two different strategies : successive application of

1 \rightarrow 2

optimal cloning machines and application of

1 \rightarrow 3

optimal cloning machines. Interestingly, we show that

1 \rightarrow 3

optimal cloner does a better job at broadcasting than the successive application of

1 \rightarrow 2

cloners. Finally, we create an example to show that there are local unitaries, which when applied on non-maximally entangled state locally give us a better range of broadcasting, that surpasses the best possible range obtained using cloning machines. This result opens up a new direction in exploration of methods to perform broadcasting which may outperform standard broadcasting strategies implemented through cloning transformations.

We investigate the optimal distribution of quantum information over multipartite systems in asymmetric settings. We introduce cloning transformations that take

N

identical replicas of a pure state in any dimension as input and yield a collection of clones with nonidentical fidelities. As an example, if the clones are partitioned into a set of

{M}_{A}

clones with fidelity

{F}^{A}

and another set of

{M}_{B}

clones with fidelity

{F}^{B}

, the trade-off between these fidelities is analyzed, and particular cases of optimal $N\ensuremath{\rightarrow}{M}_{A}+{M}_{B}$ cloning machines are exhibited. We also present an optimal $1\ensuremath{\rightarrow}1+1+1$ cloning machine, which is an example of a tripartite fully asymmetric cloner. Finally, it is shown how these cloning machines can be optically realized.