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arXiv:quant-ph/9701028 · Physical Review A

Broadcasting of entanglement via local copying

Vladimír Bužek, Vlatko Vedral, Martin Bodo Plenio, P. L. Knight, Mark S. Hillery

Published May 1, 1997• 95 citations
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Abstract

We show that inseparability of quantum states can be partially broadcasted (copied or cloned) with the help of local operations, i.e., distant parties sharing an entangled pair of spin-1/2 states can generate two pairs of partially nonlocally entangled states using only local operations. This procedure can be viewed as an inversion of quantum purification procedures.

DOI
10.1103/physreva.55.3327

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We show that inseparability of quantum states can be partially broadcasted (copied or cloned) with the help of local operations, i.e., distant parties sharing an entangled pair of spin-1/2 states can generate two pairs of partially nonlocally entangled states using only local operations. This procedure can be viewed as an inversion of quantum purification procedures.
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.
In this work, we extensively study the problem of broadcasting of quantum correlations (QCs). This includes broadcasting of quantum entanglement as well as correlations that go beyond the notion of entanglement (QCsbE). It is quite well known from the ``no-broadcasting theorem'' that perfect broadcasting of QCs is not possible. However, it does not rule out the possibility of partial broadcasting of QCs where we can get lesser correlated states from a given correlated state. In order to have a holistic view of broadcasting, we investigate this problem by starting with a most general representation of two qubit mixed states in terms of the Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (BH) cloner both locally and nonlocally. Unlike entanglement, we find that it is impossible to broadcast QCsbE optimally. Lastly, we generalize these results for any symmetric or asymmetric cloning machines as well. This result brings out a fundamental difference between the correlations defined from the perspective of entanglement and the correlations measure which claims to go beyond entanglement.
We present an example for broadcasting of the entanglement of a two-mode squeezed state of the electromagnetic field shared by two distant parties into two nonlocal bipartite entangled states. Using the technique of covariance matrices we demonstrate the entanglement between the nonlocal output modes and the separability of the local output modes. We find the range of values for the squeezing parameter and the amplifier phase for which broadcasting of continuous-variable entanglement can be implemented for physical states.
In this work, we investigate the problem of a secretly broadcasting of a three-qubit entangled state between two distant partners. The interesting feature of this problem is that starting from two-particle entangle states shared between two distant partners we find that the action of a local cloner on the qubits and the measurement on the machine state vector generates three-qubit entanglement between them. The broadcasting of entanglement is made secret by sending the measurement result secretly using cryptographic scheme based on orthogonal states. Further we show that this idea can be extended to generate three-particle entangled states between three distant partners.