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The roles of quantum correlations in quantum cloning

Jun Zhang, Shao-xiong Wu, Chang-shui Yua

Published Aug 17, 2016• 0 citations
OpenAlex

Abstract

In this paper, we study the entanglement and quantum discord of the output modes in the unified 1 → 2 state-dependent cloning and probabilistic quantum cloning. The tripartite entanglement among the output modes and the quantum cloning machine is also considered. We find that the roles of the quantum correlations including the bipartite and tripartite entanglement and quantum discord strongly depend on the quantum cloning machines as well as the cloned state. In particular, it is found that this quantum cloning scheme can be realizable even without any quantum correlation.

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arXiv:1807.11002•Physical Review A•Oct 18, 2019•7 citations
In this paper, we study the entanglement and quantum discord of the output modes in the unified 1 → 2 state-dependent cloning and probabilistic quantum cloning. The tripartite entanglement among the output modes and the quantum cloning machine is also considered. We find that the roles of the quantum correlations including the bipartite and tripartite entanglement and quantum discord strongly depend on the quantum cloning machines as well as the cloned state. In particular, it is found that this quantum cloning scheme can be realizable even without any quantum correlation.
We utilize quantum discord to charecterize the correlation present in Buzek-Hillery quantum copying machine \cite{bh} (not necessarily universal quantum cloning machine). In other words we quantify the correlation present beetween the original and the replicated copy of the quantum state obtained at the outport port, Interestingly, we find some domain of the machine parameter, for which the quantum disord is non negative even in the mere absence of entanglement. These non zero values of the quantum discord is a strong signature for the presence of non classical correlations. This is one step forward evidence in the support of the fact that quantum discord and entanglement are not synonymous.
We apply the local optimal universal asymmetric cloning machine on an initially pure entangled state of two qubits. As output, we obtain two final states which present quantum correlations. We analyze three types of quantum correlations among the final states, namely, concurrence, quantum discord, and consonance. A detailed comparison between concurrence, quantum discord, and consonance is made, and we find that consonance is greater than quantum discord, which is in turn greater than concurrence.
Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: ``Is there an optimal quantum cloning machine?'' Buzek and Hillery answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.
Recently Galvão and Hardy have shown that quantum cloning can improve the performance of some quantum computation tasks. However such performance enhancement is possible only if quantum correlations survive the cloning process. We investigate preservation of the quantum correlations in the process of non-local cloning of entangled pairs of two-level systems. We consider different kinds of quantum cloning machines and compare their effectiveness in the cloning of non-maximally entangled pure states. A mean entanglement is introduced in order to obtain a quantitative evaluation of an average efficiency for the different cloning machines. We show that a reduction of the quantum correlations is significant and it strongly depends upon the kind of cloning machine used. Losses of the entanglement are largest in the case of the universal quantum cloning machine. Generally, in all cases considered the losses of the entanglement are so drastic that the method of enhancement for the performance of the quantum computation using quantum cloning seems to be questionable.
Recently Galvão and Hardy have shown that quantum cloning can improve the performance of some quantum computation tasks. However such performance enhancement is possible only if quantum correlations survive the cloning process. We investigate preservation of the quantum correlations in the process of non-local cloning of entangled pairs of two-level systems. We consider different kinds of quantum cloning machines and compare their effectiveness in the cloning of non-maximally entangled pure states. A mean entanglement is introduced in order to obtain a quantitative evaluation of an average efficiency for the different cloning machines. We show that a reduction of the quantum correlations is significant and it strongly depends upon the kind of cloning machine used. Losses of the entanglement are largest in the case of the universal quantum cloning machine. Generally, in all cases considered the losses of the entanglement are so drastic that the method of enhancement for the performance of the quantum computation using quantum cloning seems to be questionable.
Quantum mechanical properties like entanglement, discord, and coherence act as fundamental resources in various quantum information processing tasks. Consequently, the technique of generating more resources from a few, typically termed as broadcasting, serves as a promising candidate for the design of quantum networks. One way to broadcast resources could be using a cloning operation. In this article, broadcasting of quantum resources beyond $2\ensuremath{\bigotimes}2$ systems is investigated. In particular, in $2\ensuremath{\bigotimes}3$ dimensions, a class of states not useful for broadcasting of entanglement is characterized considering an optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states and two-parameter class of states are obtained to exemplify our protocol. A significant derivative of our protocol is that the cloning operation generates a qutrit ($3\ensuremath{\bigotimes}3$) entangled pair with positive partial transpose on one of the local sides, and an absolutely separable qubit ($2\ensuremath{\bigotimes}2$) pair on the other side of the input bipartite $2\ensuremath{\bigotimes}3$-dimensional resource state. Moving beyond entanglement, in $2\ensuremath{\bigotimes}d$ dimensions, the impossibility to optimally broadcast quantum discord and quantum coherence (l1{l}_{1}l1​ norm) is established. However, some significant illustrations are provided to highlight that nonoptimal broadcasting of discord and coherence is still possible.