Dynamics of the nonlocality measured by the violation of Svetlichny's Bell-type inequality is investigated in the non-Markovian model. The phenomenon of nonlocality sudden birth for the atoms and the reservoirs is obtained. The evolution of the nonlocality among the atoms or the reservoirs depends on the choice of the atom detuning from the cavity pseudomode, the cavity pseudomode decay and the rotation angles. For the small pseudomode decay in the near-resonance regime, the initial atomic nonlocality is completely transferred to the reservoirs ultimately.
Measurement-induced nonlocality is a measure of nonlocalty introduced by Luo and Fu [Phys. Rev. Lett \textbf{106}, 120401 (2011)]. In this paper, we study the problem of evaluation of Measurement-induced nonlocality (MIN) for an arbitrary
m×n dimensional bipartite density matrix
ρ for the case where one of its reduced density matrix,
ρa, is degenerate (the nondegenerate case was explained in the preceding reference). Suppose that, in general,
ρa has
d degenerate subspaces with dimension
mi(mi≤m,i=1,2,...,d). We show that according to the degeneracy of
ρa, if we expand
ρ in a suitable basis, the evaluation of MIN for an
m×n dimensional state
ρ, is degraded to finding the MIN in the
mi×n dimensional subspaces of state
ρ. This method can reduce the calculations in the evaluation of MIN. Moreover, for an arbitrary
m×n state
ρ for which
mi≤2, our method leads to the exact value of the MIN. Also, we obtain an upper bound for MIN which can improve the ones introduced in the above mentioned reference. In the final, we explain the evaluation of MIN for
3×n dimensional states in details.
Measurement-induced nonlocality is a measure of nonlocalty introduced by Luo and Fu [Phys. Rev. Lett \textbf{106}, 120401 (2011)]. In this paper, we study the problem of evaluation of Measurement-induced nonlocality (MIN) for an arbitrary
m×n dimensional bipartite density matrix
ρ for the case where one of its reduced density matrix,
ρa, is degenerate (the nondegenerate case was explained in the preceding reference). Suppose that, in general,
ρa has
d degenerate subspaces with dimension
mi(mi≤m,i=1,2,...,d). We show that according to the degeneracy of
ρa, if we expand
ρ in a suitable basis, the evaluation of MIN for an
m×n dimensional state
ρ, is degraded to finding the MIN in the
mi×n dimensional subspaces of state
ρ. This method can reduce the calculations in the evaluation of MIN. Moreover, for an arbitrary
m×n state
ρ for which
mi≤2, our method leads to the exact value of the MIN. Also, we obtain an upper bound for MIN which can improve the ones introduced in the above mentioned reference. Finally, we explain the evaluation of MIN for
3×n dimensional states in details.
We quantify the measurement-induced nonlocality [Luo and Fu, Phys. Rev. Lett. 106, 120401 (2011)] from the perspective of the relative entropy. This quantification leads to an operational interpretation for the measurement-induced nonlocality, namely, it is the maximal entropy increase after the locally invariant measurements. The relative entropy of nonlocality is upper bounded by the entropy of the measured subsystem. We establish a relationship between the relative entropy of nonlocality and the geometric nonlocality based on the Hilbert-Schmidt norm, and show that it is equal to the maximal distillable entanglement. Several trade-off relations are obtained for tripartite pure states. We also give explicit expressions for the relative entropy of nonlocality for Bell-diagonal states.
Measurement-Induced NonLocality was introduced by Luo and Fu (Phys. Rev. Lett. \textbf{106}, 120401,(2011)) as a measure of nonlocality in a bipartite state. In this paper we will discuss monogamy property of measurement-induced nonlocality for some three- and four-qubit classes of states. Unlike discord, we find quite surprising results in this situation. Both the GHZ and W states satisfy monogamy relations in the three-qubit case, however, in general there are violations of monogamy relations in both the GHZ-class and W-class states. In case of four-qubit system, monogamy holds for most of the states in the generic class. Four qubit GHZ does not satisfy monogamy relation, but W-state does. We provide several numerical results including counterexamples regarding monogamy nature of measurement induced nonlocality. We will also extend our results of generalized W-class to n-qubit.
Measurement-induced nonlocality is a measure of nonlocality introduced recently by Luo and Fu. We present here sufficient and necessary conditions for a quantum state for which this quantity is equal to zero. Furthermore it is shown that for such a state ?ab with any local channel acting on Ha cannot create measurement-induced nonlocality if and only if either it is a completely contractive channel or it is a nontrivial isotropic channel. For the qubit case this property is an additional characteristic of the completely contractive channel or the commutativity-preserving unital channel.