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arXiv:1310.5119 · Physical Review A

Generation of multipartite spin entanglement from multimode squeezed states

Niranjan Sridhar, Olivier Pfister

Published Jan 13, 2014• 3 citations
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Abstract

We investigate the systematic use of the Schwinger representation, by virtue of which two boson fields are equivalent to an effective spin, for casting multimode squeezed states into multipartite spin entangled states. The motivation for this endeavor is the following established fact: finitely squeezed, two-mode entangled states can be recast into maximally entangled bipartite spin states, irrespective of their level of squeezing (in the lossless case). This work explores the generalization of this interesting property to multipartite entanglement. While we found that the generalization of multipartite Gaussian entanglement to multipartite spin entanglement is not straightforward, there are nonetheless interesting features and entangled states to be found. Here we study a few continuous-variable entangled states already realized experimentally, and show that some of them correspond to multipartite spin entangled states.

DOI
10.1103/physreva.89.012310

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We investigate the systematic use of the Schwinger representation, by virtue of which two boson fields are equivalent to an effective spin, for casting multimode squeezed states into multipartite spin entangled states. The motivation for this endeavor is the following established fact: finitely squeezed, two-mode entangled states can be recast into maximally entangled bipartite spin states, irrespective of their level of squeezing (in the lossless case). This work explores the generalization of this interesting property to multipartite entanglement. While we found that the generalization of multipartite Gaussian entanglement to multipartite spin entanglement is not straightforward, there are nonetheless interesting features and entangled states to be found. Here we study a few continuous-variable entangled states already realized experimentally, and show that some of them correspond to multipartite spin entangled states.
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We present several measurement schemes for accessing separability criteria for continuous-variable bipartite quantum systems. Starting from moments of the bosonic mode operators, criteria suitable to witness entanglement are expressed in terms of multimode spin observables via the Jordan-Schwinger map. These observables are typically defined over a few replicas of the state of interest and can be transformed into simple photon number measurements by passive optical circuits. Our measurement schemes require only a handful of measurements, thereby allowing one to efficiently detect entanglement without the need for costly state tomography as illustrated for a variety of physically relevant states (Gaussian, mixed Schr\"odinger cat, and NOON states). The influence of typical experimental imperfections is shown to be moderate.
We propose a scheme for generating bipartite and multipartite entangled squeezed states via the Jaynes-Cummings model with large detuning. Bipartite entanglement of these entangled states is quantified by the concurrence. We also use the N -tangle to compute multipartite entanglement of these multipartite entangled squeezed states. Finally we discuss two limiting cases which arise from r →∞ and r →0, in which the multipartite entangled squeezed state reduces correspondingly into an N -qubit Greenberger-Horne-Zeilinger state and an N -qubit W state.
We show that the best way to study the relationship between quantum entanglement and quantum squeezing for the multimode case is through constructing the new n -pair entangled state representation . The explicit form of the 2 n -mode squeezing operator which squeezes the n -pair entangled state can be directly derived via the transition from to where M is an n × n complex matrix, and the technique of integration within an ordered product of operators. We also analyze the squeezing properties of the 2 n -mode squeezed state for M being Hermitian, and obtain the variances of the 2 n -mode quadrature operators in the 2 n -mode squeezed vacuum state with a concise result; the condition for reaching the minimum of the uncertainty relationship is also investigated.