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arXiv:0812.0967

Secret Broadcasting of GHZ type state

Indranil Chakrabarty

Published Dec 4, 2008• 0 citations
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Abstract

Here we described a protocol by which one can broadcast GHZ-type states secretly. We have done this with the help of a cloning machine followed by subsequent measurements. We also made a comparative study of the amount of residual tangle present in these entangled states, obtained as outputs of the measurements.
DOI
10.48550/arxiv.0812.0967

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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 exhaustively investigate $1\ensuremath{\rightarrow}2$ local and nonlocal broadcasting of entanglement as well as correlations beyond entanglement (geometric discord) using asymmetric Pauli cloners with the most general two-qubit state as the resource. We exemplify asymmetric broadcasting of entanglement using ``maximally entangled mixed states.'' We demonstrate the variation of broadcasting range with the amount of entanglement present in the resource state as well as with the asymmetry in the cloner. We show that it is impossible to optimally broadcast geometric discord with the help of these asymmetric Pauli cloning machines. We also study the problem of $1\ensuremath{\rightarrow}3$ broadcasting of entanglement using nonmaximally entangled state as the resource. For this task, we introduce a method we call successive broadcasting which involves application of $1\ensuremath{\rightarrow}2$ optimal cloning machines multiple times. We compare and contrast the performance of this method with the application of direct $1\ensuremath{\rightarrow}3$ optimal cloning machines. We show that $1\ensuremath{\rightarrow}3$ optimal cloner does a better job at broadcasting than the successive application of $1\ensuremath{\rightarrow}2$ cloners and the successive method can be beneficial in the absence of $1\ensuremath{\rightarrow}3$ cloners. We also bring out the fundamental difference between the tasks of cloning and broadcasting in the final part of the paper. We create examples to show that there exist local unitaries which can be employed to give a better range for broadcasting. Such unitary operations are not only economical, but also surpass the best possible range obtained using existing cloning machines enabling broadcasting of lesser entangled states. This result opens up a direction in exploration of methods to facilitate broadcasting which may outperform the standard strategies implemented through cloning transformations.