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arXiv:quant-ph/0210038

Disentangling and broadcasting an entangled state simultaneously by asymmetric cloning

Ya-Fei Yu, Jian Feng, Zhou, Xiaoqing, Mingsheng Zhan

Published Oct 6, 2002• 0 citations
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Abstract

We construct a quantum machine which, by using asymmetric cloner, deals with disentangling and broadcasting entanglement in a single unitary evolution. The attainable maximum value of the scaling parameter $s$ for disentangling is identical to that obtained in previous works. The fidelity of the cloning state with respect to the input entangled state is state-dependent.

DOI
10.48550/arxiv.quant-ph/0210038

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arXiv:1604.04995•Physical Review A•Nov 9, 2016•1 citation
We construct a quantum machine which, by using asymmetric cloner, deals with disentangling and broadcasting entanglement in a single unitary evolution. The attainable maximum value of the scaling parameter sss for disentangling is identical to that obtained in previous works. The fidelity of the cloning state with respect to the input entangled state is state-dependent.
We establish the best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two nonorthogonal states and discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive an upper bound on the quantum capacity of the depolarizing quantum channel.
In this work, we exhaustively investigate 1→21 \rightarrow 21→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→31 \rightarrow 31→3 broadcasting of entanglement using non-maximally entangled state (NME) as a resource. We adopt two different strategies : successive application of 1→21 \rightarrow 21→2 optimal cloning machines and application of 1→31 \rightarrow 31→3 optimal cloning machines. Interestingly, we show that 1→31 \rightarrow 31→3 optimal cloner does a better job at broadcasting than the successive application of 1→21 \rightarrow 21→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.
In this work, we extensively study the problem of broadcasting of entanglement. In the first part of the work, we reconceptualize the idea of state dependent quantum cloning machine, and in that process we introduce different types of state dependent cloners like static and dynamic state dependent cloners. We derive the conditions under which we can make these cloners independent of the input state. In the broadcasting part, as our resource initial state, we start with general two qubit state and consider specific examples like, non maximally entangled state (NME), Werner like state (WS), and Bell diagonal state (BDS). We apply both state dependent/ state independent cloners, both locally and non-locally, in each of these cases. Incidentally, we find several instances where state dependent cloners outperform state independent cloners in broadcasting. This work gives us a holistic view on the broadcasting of entanglement in various two qubit states, when we have an almost exhaustive sets of cloning machines in our arsenal
Suppose we are given an entangled pair and asked how well we can produce two entangled pairs starting from a given entangled pair using only local operations. To respond to this question, we study broadcasting of entanglement using a state-dependent quantum cloning machine as a local copier. We show that the length of the interval for probability-amplitude-squared α 2 for broadcasting of entanglement using a state-dependent cloner can be made larger than the length of the interval for probability-amplitude-squared for broadcasting entanglement using a state-independent cloner. Further we show that there exists a local state-dependent cloner which gives better quality copy (in terms of average fidelity) of an entangled pair than the local universal cloner.
We present a unified universal quantum cloning machine, which combines several different existing universal cloning machines together, including the asymmetric case. In this unified framework, the identical pure states are projected equally into each copy initially constituted by input and one half of the maximally entangled states. We show explicitly that the output states of those universal cloning machines are the same. One importance of this unified cloning machine is that the cloning procession is always the symmetric projection, which reduces dramatically the difficulties for implementation. Also, it is found that this unified cloning machine can be directly modified to the general asymmetric case. Besides the global fidelity and the single-copy fidelity, we also present all possible arbitrary-copy fidelities.
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.