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arXiv:0708.1869 · Physical Review A

Broadcasting of continuous-variable entanglement

Satyabrata Adhikari, A. S. Majumdar, N. Nayak

Published Apr 1, 2008• 16 citations
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Abstract

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.

DOI
10.1103/physreva.77.042301

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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.
We consider two-mode squeezed states which are parametrized by the squeezing parameter and the phase. We present a scheme for teleporting such entangled states of continuous variables from Alice to Bob. Our protocol is operationalized through the creation of a four-mode entangled state shared by Alice and Bob using linear amplifiers and beam splitters. Teleportation of the entangled state proceeds with local operations and the classical communication of four bits. We compute the fidelity of teleportation and find that it exhibits a trade-off with the magnitude of entanglement of the resultant teleported state.
Experimental demonstration of quantum entanglement among more than two quantum systems with continuous spectra is summarized in the paper. The tripartite entangled state, named also GHZ-like state, is produced by distributing a two-mode squeezed state light to three parties using beamsplitter. A nondegenerate optical parameter amplifier (NOPA) operating at deamplification serves as the initial bipartite entanglement source. The output optical modes from the NOPA are a pair of bright EPR entangled beams with orthogonal polarizations, anticorrelated amplitude quadratures and correlated phase quadratures. The results confirm the existence of the quantum correlation among three amplitude quadratures of modes.
We show that two qubits can be entangled by local interactions with an entangled two-mode continuous variable state. This is illustrated by the evolution of two two-level atoms interacting with a two-mode squeezed state. Two modes of the squeezed field are injected respectively into two spatially separate cavities and the atoms are then sent into the cavities to resonantly interact with the cavity field. We find that the atoms may be entangled even by a two-mode squeezed state which has been decohered while penetrating into the cavity.
We show that two qubits can be entangled by local interactions with an entangled two-mode continuous variable state. This is illustrated by the evolution of two two-level atoms interacting with a two-mode squeezed state. Two modes of the squeezed field are injected respectively into two spatially separate cavities and the atoms are then sent into the cavities to interact resonantly with the cavity field. We find that the atoms may be entangled even by a two-mode squeezed state which has been decohered while penetrating into the cavity.
Continuous variable (CV) entanglement refers to the type of entanglement of quantum wave-like systems that are described by continuous variables in an inherently infinite-dimensional space. It can become a crucial resource for quantum communication, sensing, and computation. We propose the mechanism of transfer of quantum entanglement (TQE) from a nonlocal photon to two initially separate single-mode squeezed vacuum (SMSV) states. The nonlocal photon is the only original quantum resource from which entanglement is transferred to CV states of a certain parity in a deterministic manner without them directly interacting with each other. Measurement-induced CV parity entanglement is tuned using initial squeezing and the beam splitter (BS) parameter, allowing us to estimate the probability of transfer of maximum entanglement at sufficiently high brightness to be 0.2344 for initial SMSV states. If, instead of the original SMSV states, we use those from which one photon is initially subtracted, then the heralded technique can turn the maximum entanglement probabilistic transfer protocol into a nearly deterministic one, the probability of which is >0.98. Such a perfect TQE from the nonlocal photon to a maximally parity-entangled CV state can be considered the most suitable for applications, since it preserves the trade-off between the probability of its implementation and brightness of the output non-Gaussian states.