Multipartite quantum correlation (MQC) not only explains many novel microscopic and macroscopic quantum phenomena, but also holds promise for specific quantum technologies with superiorities. MQCs descriptions and measures have been an open topic, due to their rich and complex organization and structure. Here reconsidering MQC descriptions and their practical applications in some quantum technologies, we propose a novel description called multipartite two-partite QC, which provides an intuitive and clear physical picture. Specifically, we present three types of measures: one class based on minimal entropy-like difference of local measurement fore-and-aft multipartite two-partite density matrix such as multipartite two-partite quantum discord (QD), another class based on minimal trace-like geometric distance such as multipartite two-partite Hilbert-Schmidt Distance (HSD), and a third class based on decoherence such as multipartite two-partite Local Measurement-Induced Minimal Decoherence (LMIMD) and Local Eigen-Measurement-Induced Decoherence (LEMID). Their computations required for these measures are relatively easy. All of the advantages make them promising candidates for specific potential applications in various quantum technologies. Finally, we employ these three types of measures to explore the organization and structure of some typical genuine MQCs, and analyze their relative characteristics based on their physical implications and mathematical structures.
Multipartite quantum correlation (MQC) not only explains many novel microscopic and macroscopic quantum phenomena, but also holds promise for specific quantum technologies with superiorities. MQCs descriptions and measures have been an open topic, due to their rich and complex organization and structure. Here reconsidering MQC descriptions and their practical applications in some quantum technologies, we propose a novel description called multipartite two-partite QC, which provides an intuitive and clear physical picture. Specifically, we present three types of measures: one class based on minimal entropy-like difference of local measurement fore-and-aft multipartite two-partite density matrix such as multipartite two-partite quantum discord (QD), another class based on minimal trace-like geometric distance such as multipartite two-partite Hilbert-Schmidt Distance (HSD), and a third class based on decoherence such as multipartite two-partite Local Measurement-Induced Minimal Decoherence (LMIMD) and Local Eigen-Measurement-Induced Decoherence (LEMID). Their computations required for these measures are relatively easy. All of the advantages make them promising candidates for specific potential applications in various quantum technologies. Finally, we employ these three types of measures to explore the organization and structure of some typical genuine MQCs, and analyze their relative characteristics based on their physical implications and mathematical structures.
In this paper, we present a measure of quantum correlation for a multipartite system, defined as the sum of the correlations for all possible partitions. Our measure can be defined for quantum discord (QD), geometric quantum discord or even for entanglement of formation (EOF). For tripartite pure states, we show that the multipartite measures for the QD and the EOF are equivalent, which allows direct comparison of the distribution and the robustness of these correlations in open quantum systems. We study dissipative dynamics for two distinct families of entanglement: a W state and a GHZ state. We show that, for the W state, the QD is more robust than the entanglement, while for the GHZ state, this is not true. It turns out that the initial genuine multipartite entanglement present in the GHZ state makes the EOF more robust than the QD.
Quantum coherence and quantum correlations are of fundamental and practical significance for the development of quantum mechanics.They are also cornerstones of quantum computation and quantum communication theory. Searching physically meaningful and mathematically rigorous quantifiers of them are long-standing concerns of the community of quantum information science, and various faithful measures have been introduced so far. We review in this paper the measures of discordlike quantum correlations for bipartite and multipartite systems, the measures of quantum coherence for any single quantum system, and their relationship in different settings. Our aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states. We discuss the interrelations between quantum coherence and quantum correlations established in an operational way, and the fundamental characteristics of quantum coherence such as their complementarity under different basis sets, their duality with path information of an interference experiment, their distillation and dilution under different operations, and some new viewpoints of the superiority of the quantum algorithms from the perspective of quantum coherence. Additionally, we review properties of geometric quantum correlations and quantum coherence under noisy quantum channels. Finally, the main progresses for the study of quantum correlations and quantum coherence in the relativistic settings are reviewed. All these results provide an overview for the conceptual implications and basic connections of quantum coherence, quantum correlations, and their potential applications in various related subjects of physics.
The main concern of this paper is how to define proper measures of multipartite entanglement for mixed quantum states. Since the structure of partial separability and multipartite entanglement is getting complicated if the number of subsystems exceeds two, one cannot expect the existence of an ultimate scalar entanglement measure, which grasps even a small part of the rich hierarchical structure of multipartite entanglement, and some higher-order structure characterizing that is needed. In this paper we make some steps in this direction. First, we reveal the lattice-theoretic structure of the partial separability classification, introduced earlier [Sz. Szalay and Z. K\"ok\'enyesi, Phys. Rev. A 86, 032341 (2012)]. It turns out that, mathematically, the structure of the entanglement classes is the up-set lattice of the structure of the different kinds of partial separability, which is the down-set lattice of the lattice of the partitions of the subsystems. It also turns out that, physically, this structure is related to the local operations and classical communication convertibility: If a state from a class can be mapped into another one, then that class can be found higher in the hierarchy. Second, we introduce the notion of multipartite monotonicity, expressing that a given set of entanglement monotones, while measuring the different kinds of entanglement, shows also the same hierarchical structure as the entanglement classes. Then we construct such hierarchies of entanglement measures and propose a physically well-motivated one, being the direct multipartite generalization of the entanglement of formation based on the entanglement entropy, motivated by the notion of statistical distinguishability. The multipartite monotonicity shown by this set of measures motivates us to consider the measures to be the different manifestations of some ``unified'' notion of entanglement.
Abstract We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking.
By using measurement-induced disturbance (S Luo 2008 Phys. Rev. A 77 022301 ), we propose a quantifier for genuine multipartite quantum correlations. The connection between this quantum correlations measure and the quantum advantage in multiport dense coding for pure three-qubit states is established. It is also used to investigate the dynamics of quantum correlations in a four-partite system. The phenomena of generation of quantum correlations and holding of quantum correlations in some time windows are found. As a byproduct, the monogamy score based on measurement-induced disturbance is related to the generalized geometric measure for pure three-qubit states.
Repeatedly in the field of Quantum Information Science (QIS) it’s essentially required of physical systems the quantification concerning its quantum phenomena, such as Quantum Coherence (QC) relying in quantum superposition states. Hereafter several quantifiers of QC have been proposed over the years through distance measures in quantum state spaces, called distinguishability measures, playing an important role in QIS correlation phenomena such as Discord and Entanglement with Quantum Cryptography implementation, as example. The aim of this dissertation is to extend the research of QC, published by Jonas Maziero in an article, performing an in-depth analysis regarding the control of local and non-local aspects of Hilbert-Schmidt Coherence (HSC) in multipartite systems and its relations with others QC quantifiers, as well as an analisys of a possible Hilbert-Schmidt Distance (HSD) implication in QC functions over the Non-Monotonicity under Tensor Products (NMuTP) inequality and of limitations between Coherence of state populations and energy. Starting from the generic multipartite state of level quantum energy systems (qudit), defined from the Bloch parameterization, calculations of QC functions concerning its particular cases are considered for 1-qubit, 2-qubit, 1-qutrit and two copies of 1-qubit adopting HSD. Writing the HSC function for the latter case in terms of its local and non-local parts and from the result of 1-qubit it is possible, by manipulating the difference between local populations, to infer a non-local implication in the HSC for that system, in contrast to what has been seen by adopting distinct dissimilarity measures for this function, named l1- Norm Distance and Relative Entropy Distance, cases where there are no implications and where there is a direct consequence with their local populations instead of the previously difference between them, respectively. Notwithstanding, HSD usage provides a description of an awkward relation in QIS towards NMuTP, and a possible implication of that kind of relation in QIS emergent phenomena such as QC function.