Quantifying geometric measure of entanglement by mean value of spin and spin correlations with application to physical systems

Abstract

We quantify the geometric measure of entanglement in terms of mean values of observables of entangled system. For pure states we find the relation of geometric measure of entanglement with the mean value of spin one-half for the system composed of spin and arbitrary quantum system. The geometric measure of entanglement for mixed states of rank-2 is studied as well. We find the explicit expression for geometric entanglement and the relation of entanglement in this case with the values of spin correlations. These results allow to find experimentally the value of entanglement by measuring a value of the mean spin and the spin correlations for pure and mixed states, respectively. The obtained results are applied for calculation of entanglement during the evolution in spin chain with Ising interaction , two-spin Ising 1 model in transverse fluctuating magnetic field, Schrödinger cat in fluctuating magnetic field.

Preparation and study of the entanglement of the Schrödinger cat state on the ibmq-melbourne quantum computer

“…Using the protocol developed in paper [12] we study the entanglement of the Schrödinger cat state. [12] q [13] q [14] q [9] Figure 3. Circuit for the preparation and measurement of the 15-qubit Schrödinger cat state.…”

“…0 is the initial state of IBM Q devices. To identify the entanglement between a certain qubit and the other qubits of the system we use the geometric measure of entanglement which can be written as follows [13,16,17]:…”

Measuring distance between quantum states on a quantum computer

“…The concept of a distance between quantum states in Hilbert space [1][2][3] has found its application in different fields of quantum mechanics related to the evolution of quantum systems [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], quantum entanglement [8,[20][21][22][23][24][25][26][27][28][29][30], quantum computations [31][32][33][34][35], etc. It was shown that the distance, which the quantum system passes during the evolution in the Hilbert space, is related to the integral of the uncertainty of energy that in turn defines the speed of evolution [4].…”

Geometric measure of entanglement of multi-qubit graph states and its detection on a quantum computer

“…Studies of entanglement of quantum states and its quantifying on a quantum computer have received much attention (see, for instance, [1,2,3,4,5,6,7,8,9,10,11,12,13,14] and references therein). Entanglement corresponds to non-classical correlations between the subsystems and presupposes that the state of a system cannot be factorized [1].…”

“…The authors of paper [8] showed that the geometric measure of entanglement of a spin one-half (or qubit) with a quantum system in a pure state |ψ is entirely determined by the mean spin in this state. Namely the following relation is satisfied…”