Here, we show that partial transposition, which is initially introduced to study entanglement, can also inspire many results on quantum discord, including (I) a discord criterion of a spectrum invariant under partial transposition, stating that one state must contain discord if its spectrum is changed by the action of partial transposition, and (II) an approach to estimate the geometric quantum discord and the one-way deficit based on the change of the spectrum. To compare with entanglement theory, we also lower bound the geometric quantum entanglement and the entanglement of relative entropy. Thus, on one hand, we illustrate an approach to specify and estimate discord based on partial transposition. On the other hand, we show that, entanglement and discord, two basic notions of nonclassical correlations, can be placed on the same ground such that their interplay and distinction can be illustrated within a universal framework.
Here, we show that partial transposition, which is initially introduced to study entanglement, can also inspire many results on quantum discord, including (I) a discord criterion of a spectrum invariant under partial transposition, stating that one state must contain discord if its spectrum is changed by the action of partial transposition, and (II) an approach to estimate the geometric quantum discord and the one-way deficit based on the change of the spectrum. To compare with entanglement theory, we also lower bound the geometric quantum entanglement and the entanglement of relative entropy. Thus, on one hand, we illustrate an approach to specify and estimate discord based on partial transposition. On the other hand, we show that, entanglement and discord, two basic notions of nonclassical correlations, can be placed on the same ground such that their interplay and distinction can be illustrated within a universal framework.
Here, we show that partial transposition, which is initially introduced to study entanglement, can also inspire many results on quantum discord including: (I) a discord criterion of spectrum invariant under partial transposition, stating that one state must contain discord if its spectrum is changed by the action of partial transposition, (II) an approach to estimate the geometric quantum discord and the one-way deficit based on the change of spectrum. To compare with entanglement theory, we also lower-bound the geometric quantum entanglement and the entanglement of relative entropy. Thus, on one hand, we illustrate an approach to specify and estimate discord based on partial transposition. On the other hand, we show that, entanglement and discord, two basic notions of nonclassical correlations, can be placed on the same ground such that their interplay and distinction can be illustrated in within a universal framework.
Quantum discord goes beyond entanglement and exists in a wide range of quantum states that may be separable, playing a crucial role in quantum information tasks. In this paper, we firstly proposed a zero-discord criterion for two-qubit system based on the partial transposition of density matrix, and then extended it to the qubit–qudit system. By detailed examples we demonstrate the effectiveness of these criteria in detecting discord. Moreover, we provide an analytical lower bound of geometric quantum discord(GQD) using eigenvalue vectors of density matrix. Finally, we presented a one-way work deficit lower bound based on our lower bound of GQD.
Quantum discord goes beyond entanglement and exists in a wide range of quantum states that may be separable, playing a crucial role in quantum information tasks. In this paper, we firstly proposed a zero-discord criterion for two-qubit system based on the partial transposition of density matrix, and then extended it to the qubit-qudit system. By detailed examples we demonstrate the effectiveness of these criteria in detecting discord. Moreover, we provide an analytical lower bound of geometric quantum discord(GQD) using eigenvalue vectors of density matrix. Finally, we presented a one-way work deficit lower bound based on our lower bound of GQD.
Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.
The characterization and quantification of quantum correlations, which play an instrumental role in exploring and exploiting the quantum world, have been extensively and intensively studied in the past few decades. Of special prominence and significance are the concepts of entanglement and discord, which are usually regarded as very distinctive quantum correlations, with the latter going beyond the former. In this work we establish a direct and natural link between entanglement and discord via state extensions and reveal that entanglement is actually the intrinsic discord, by which we mean that entanglement is the irreducible residue of discord viewed from ambient spaces. Our approach, taking into account the contextuality of a quantum state and being of a global nature, stands in sharp contrast to the local operations and classical communication paradigm of entanglement, which focuses on the state itself via a local approach. Furthermore, we introduce a figure of merit which, on the one hand, captures the essence of entanglement, i.e., nonlocality and quantumness of correlations, and, on the other hand, leads to a quantitative decomposition of total correlations into classical correlations, dissonance, and entanglement. This demystifies the meaning of entanglement from the perspective of quantum measurements and provides a unified framework for the interplay of various correlations in terms of quantum measurements and mutual information.
Quantum correlation is a key to our understanding of quantum physics. In particular, it is essential for the powerful applications to quantum information and quantum computation. There exist quantum correlations beyond entanglement, such as quantum discord (QD) and measurement-induced nonlocality (MiN) [Phys. Rev. Lett. \textbf{106}, 120401(2011)]. In [Phys. Rev. A \textbf{77}, 022113(2008)], a subclass of PPT states so-called strong positive partial transposition (SPPT) states was introduced and it was conjectured there that SPPT states are separable. However, it was illustrated with examples in [Phys. Rev. A \textbf{81}, 064101(2010)] that this conjecture is not true. Viewing the original SPPT as SPPT up to part B, in the present paper, we define SPPT state up to part A and B respectively and present a separable class of SPPT states, that is the super SPPT (SSPPT) states, in terms of local commutativity. In addition, classical-quantum (CQ) states and nullity of MiN are characterized via local commutativity. Based on CQ states, the geometric measure of quantum discord (GMQD) for infinite-dimensional case is proposed. Consequently, we highlight the relation among MiN, QD(GMQD), SSPPT and separability through a unified approach for both finite- and infinite-dimensional systems: zero MiN implies zero QD(GMQD), zero QD(GMQD) signals SSPPT and SSPPT guarantees separability, but the converses are not valid.