We investigate the correlation properties of separable two-qubit states with maximally mixed marginals. These states are divided to two sets with the same geometric quantum correlation. However, a closer scrutiny of these states reveals a profound difference between their quantum correlations as measured by more probing measures. Although these two sets of states are prepared by the same type of quantum operations acting on classically correlated states with equal classical correlations, the amount of final quantum correlation is different. We investigate this difference and trace it back to the hidden classical correlation which exists in their preparation process. We also compare these states with regard to their usefulness for entanglement distribution and their robustness against noise.
We investigate the correlation properties of separable two-qubit states with maximally mixed marginals. These states are divided to two sets with the same geometric quantum correlation. However, a closer scrutiny of these states reveals a profound difference between their quantum correlations as measured by more probing measures. Although these two sets of states are prepared by the same type of quantum operations acting on classically correlated states with equal classical correlations, the amount of final quantum correlation is different. We investigate this difference and trace it back to the hidden classical correlation which exists in their preparation process. We also compare these states with regard to their usefulness for entanglement distribution and their robustness against noise.
We study the relative strength of classical and quantum correlations, as measured by discord, for two-qubit states. Quantum correlations appear only in the presence of classical correlations, while the reverse is not always true. We identify the family of states that maximize the discord for a given value of the classical correlations and show that the largest attainable discord for mixed states is greater than for pure states. The difference between discord and entanglement is emphasized by the remarkable fact that these states do not maximize entanglement and are, in some cases, even separable. Finally, by random generation of density matrices uniformly distributed over the whole Hilbert space, we quantify the frequency of the appearance of quantum and classical correlations for different ranks.
We study the relative strength of classical and quantum correlations, as measured by discord, for two-qubit states. Quantum correlations appear only in the presence of classical correlations, while the reverse is not always true. We identify the family of states that maximize the discord for a given value of the classical correlations and show that the largest attainable discord for mixed states is greater than for pure states. The difference between discord and entanglement is emphasized by the remarkable fact that these states do not maximize entanglement and are, in some cases, even separable. Finally, by random generation of density matrices uniformly distributed over the whole Hilbert space, we quantify the frequency of the appearance of quantum and classical correlations for different ranks.
Abstract Understanding how correlations can be used for quantum communication protocols is a central goal of quantum information science. While many authors have linked the global measures of correlations such as entanglement or discord to the performance of specific protocols, in general the latter may require only correlations between specific observables. In this work, we first introduce a general measure of correlations for two-qubit states, based on the classical mutual information between local observables. Our measure depends on the state’s purity and the symmetry in the correlation distribution, according to which we provide a classification of maximally mixed marginal states (MMMS). We discuss the complementarity relation between correlations and coherence. By focusing on a simple yet paradigmatic example, i.e. the remote state preparation protocol, we introduce a method to systematically define the proper protocol-tailored measures of the correlations. The method is based on the identification of those correlations that are relevant (useful) for the protocol. On the one hand, the approach allows the role of the symmetry of the correlation distribution to be discussed in determining the efficiency of the protocol, both for MMMS and general two-qubit quantum states, and on the other hand, it allows an optimized protocol for non-MMMS to be devised, which is more efficient with respect to the standard one. Overall, our findings clarify how the key resources in simple communication protocols are the purity of the state used and the symmetry of the correlation distribution.
We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.
The classification of the multipartite entanglement is an important problem in quantum information theory. We propose a class of two qubit mixed states σAB=p∣χ1⟩⟨χ1∣⊗ρ1+(1−p)∣χ2⟩⟨χ2∣⊗ρ2, where ∣χ1⟩=α∣0⟩+β∣1⟩, ∣χ2⟩=β∣0⟩+(−1)nα∣1⟩. We have shown that the state σAB represent a classical state when n is odd while it represent a non-classical state when n is even. The purification of the state σAB is studied and found that the purification is possible if the spectral decomposition of the density matrices ρ1 and ρ2 represent pure states. We have established a relationship between three tangle, which measures the amount of entanglement in three qubit system and the quantity ⟨χ1∣χ2⟩, which identifies whether the two qubit mixed state is classical or non-classical. The three qubit purified state is then classified as a separable or biseparable or W-type or GHZ-type state using the quantum correlation, measured by geometric discord, of its reduced two qubit density matrix.
Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science, such as quantum communication, quantum computing, and quantum interferometry. Nevertheless, to our best knowledge, a directly or numerically computable measure for the entanglement of multipartite mixed states is still lacking. In this work, (i) we derive a measure of the degree of quantum correlation for mixed multipartite states. The latter possesses a closed-form expression valid in the general case unlike, to our best knowledge, all other known measures of quantum correlation. (ii) We further propose an entanglement measure, derived from this quantum correlation measure using a novel regularization procedure for the density matrix. Therefore, a comparison of the proposed measures, of quantum correlation and entanglement, allows one to distinguish between quantum correlation detached from entanglement and the one induced by entanglement and, hence, to identify separable but non-classical states. We have tested our quantum correlation and entanglement measures, on states well-known in literature: a general Bell diagonal state and the Werner states, which are easily tractable with our regularization procedure, and we have verified the accordance between our measures and the expected results for these states. Finally, we validate the two measures in two cases of multipartite states. The first is a generalization to three qubits of the Werner state, the second is a one-parameter three qubits mixed state interpolating between a bi-separable state and a genuine multipartite state, passing through a fully separable state.