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 ${J}_{k}$ . 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.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 ${J}_{k}$. 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.

arXiv:0806.1048Physical Review AApr 27, 2009222 citations

Probing mean values and correlations of high-spin systems on a quantum computer

Andrij Romanovych Kuzmak, V. M. Tkachuk

Abstract We consider simulation of the high spins on a quantum computer. The protocols which allow one to measure the mean value of spin and correlations between spins are proposed. As a result, we determine the time dependence of the mean values of spin-1 in the magnetic field prepared on the ibmq-santiago quantum computer. In addition, we study the evolution of two interacting spins on the ibmq-lima quantum computer. The time-dependencies of the mean value of spin-1 and correlations between these spins are detected. Finally, we generalize these protocols for the spins of arbitrary values.Abstract We consider simulation of the high spins on a quantum computer. The protocols which allow one to measure the mean value of spin and correlations between spins are proposed. As a result, we determine the time dependence of the mean values of spin-1 in the magnetic field prepared on the ibmq-santiago quantum computer. In addition, we study the evolution of two interacting spins on the ibmq-lima quantum computer. The time-dependencies of the mean value of spin-1 and correlations between these spins are detected. Finally, we generalize these protocols for the spins of arbitrary values.

arXiv:2205.10800Europhysics Letters (EPL)Nov 1, 20232 citations

Understanding the role of entanglement in quantum computing

Benoît Vermersch

Sep 1, 20220 citations

{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.