arXiv:1609.08516 · Physical Review A

Multipartite entanglement detection with nonsymmetric probing

Luca Dellantonio, Sumanta Das, J. Appel, Anders Søndberg Sørensen

Published Apr 10, 2017• 6 citations

Abstract

We show that spin-squeezing criteria commonly used for entanglement detection can be erroneous if the probe is not symmetric. We then derive a lower bound on squeezing for separable states in spin systems probed asymmetrically. Using this we further develop a procedure that allows us to verify the degree of entanglement of a quantum state in the spin system. Finally, we apply our method for entanglement verification to existing experimental data, and use it to prove the existence of tripartite entanglement in a spin-squeezed atomic ensemble.

DOI: 10.1103/physreva.95.040301

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arXiv:1609.08516 · Physical Review A

Multipartite entanglement detection with nonsymmetric probing

Luca Dellantonio, Sumanta Das, J. Appel, Anders Søndberg Sørensen

Published Apr 10, 2017• 6 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.95.040301

Related papers

Criteria to detect genuine multipartite entanglement using spin measurements

Run Yan Teh, M. D. Reid

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What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components. They can be used for the experimental detection of entanglement in a system of spin‐12 particles in which the spins cannot be individually addressed. We also show how to obtain the complete set of entanglement conditions if the mean spin and the spin correlation matrix are known. Finally, we apply our criteria for entanglement detection in spin models, showing that they can be used to detect bound entanglement in the thermal state of these systems.What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components. They can be used for the experimental detection of entanglement in a system of spin‐12 particles in which the spins cannot be individually addressed. We also show how to obtain the complete set of entanglement conditions if the mean spin and the spin correlation matrix are known. Finally, we apply our criteria for entanglement detection in spin models, showing that they can be used to detect bound entanglement in the thermal state of these systems.

AIP conference proceedingsJan 1, 20090 citations

We derive conditions in the form of inequalities to detect the genuine

N

-partite entanglement of

N

systems. The inequalities are expressed in terms of variances of spin operators and can be tested by local spin measurements performed on the individual systems. Violation of the inequalities is sufficient (but not necessary) to certify the multipartite entanglement and occurs when a type of spin squeezing is created. The inequalities are similar to those derived for continuous-variable systems, but instead are based on the Heisenberg spin-uncertainty relation $\mathrm{\ensuremath{\Delta}}{J}_{x}\mathrm{\ensuremath{\Delta}}{J}_{y}\ensuremath{\ge}|\ensuremath{\langle}{J}_{z}\ensuremath{\rangle}|/2$. We also extend previous work to derive spin-variance inequalities that certify the full tripartite inseparability or genuine multipartite entanglement among systems with fixed spin

J

, as in Greenberger--Horne--Zeilinger (GHZ) states and W states where

J=1/2

. These inequalities are derived from the planar spin-uncertainty relation ${(\mathrm{\ensuremath{\Delta}}{J}_{x})}^{2}+{(\mathrm{\ensuremath{\Delta}}{J}_{y})}^{2}\ensuremath{\ge}{C}_{J}$ where

{C}_{J}

is a constant for each

J

. Finally, it is shown how the inequalities detect multipartite entanglement based on Stokes operators. We illustrate with experiments that create entanglement shared among separated atomic ensembles, polarization-entangled optical modes, and the clouds of atoms of an expanding spin-squeezed Bose-Einstein condensate. For each example, we give a criterion to certify the mutual entanglement.

N

-qubit states. We apply our method to theoretical study of Dicke states, and, in particular, to

\mathrm{W}

states of

N

qubits. Then, we analyze the recently experimentally generated seven- and eight-ion

\mathrm{W}

states [Nature 438, 643 (2005)]. we also present some details concerning this experiment. Finally, we improve criteria for detection of genuine tripartite entanglement based on entanglement witnesses.

{J}_{k}

. They can be used for the experimental detection of entanglement in a system of spin-

\frac{1}{2}

particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of (i) the mean values and variances of

{J}_{k}

in three orthogonal directions, or (ii) the variances of

{J}_{k}

in three orthogonal directions, or (iii) the mean values of

{J}_{k}^{2}

in three orthogonal directions, or (iv) the mean values and variances of

{J}_{k}

in arbitrary directions. We compare our inequalities to known spin-squeezing entanglement criteria and discuss to which extent spin squeezing is related to entanglement in the reduced two-qubit states. Finally, we apply our criteria for the detection of entanglement in spin models, showing that they can be used to detect bound entanglement in these systems.