Quantum entanglement is the most famous type of quantum correlation between elements of a quantum system that has a basic role in quantum communication protocols like quantum cryptography, teleportation and Bell inequality detection. However, it has already been shown that various applications in quantum information theory do not require entanglement. Quantum discord as a new kind of quantum correlations beyond entanglement, is the most popular candidate for general quantum correlations. In this paper, first we find the entanglement witness in a particular multipartite quantum system which consists of a N -partite system in 2 n -dimensional space. Then we give an exact analytical formula for the quantum discord of this system. At the end of the paper, we investigate the additivity relation of the quantum correlation and show that this relation is satisfied for a N -partite system with 2 n -dimensional space.
Quantum entanglement is the most famous type of quantum correlation between elements of a quantum system that has a basic role in quantum communication protocols like quantum cryptography, teleportation and Bell inequality detection. However, it has already been shown that various applications in quantum information theory do not require entanglement. Quantum discord as a new kind of quantum correlations beyond entanglement, is the most popular candidate for general quantum correlations. In this paper, first we find the entanglement witness in a particular multipartite quantum system which consists of a N -partite system in 2 n -dimensional space. Then we give an exact analytical formula for the quantum discord of this system. At the end of the paper, we investigate the additivity relation of the quantum correlation and show that this relation is satisfied for a N -partite system with 2 n -dimensional space.
The distribution of quantum correlations in multipartite systems plays a significant role in several aspects of quantum information theory. While it is well known that these quantum correlations cannot be freely distributed, the way that they are shared in a multipartite system is an open problem even for a small set of qubits. Based on monogamylike relations between entanglement and discord for n-partite systems, we show how these correlations are distributed in general, determining distinct equalities and inequalities to the quantum discord and the entanglement of formation for arbitrary multipartite pure states.
The most common type of quantum correlations is quantum entanglement, which plays an indisputable vital role in a number of quantum information theory tasks, including quantum teleportation, quantum dense coding, and quantum cryptography. However, current findings indicate that different Entanglement is not necessary for applications in quantum information theory, and their performance can be described by a novel kind of quantum correlations that transcends entanglement. The most well-liked candidate for such widespread quantum connections is quantum discord, which Zurek first proposed more than ten years ago. We provide an overview of this current line of inquiry in this work. Following a brief overview of the fundamental ideas of quantum theory and entanglement, we introduce quantum discord and generic quantum correlations and go over three applications that are predicated on this novel kind of correlation: transmission of correlations, entanglement dispersion, and remote state preparation. We also provide an outlook for future research in this area.
Quantum entanglement is the most popular kind of quantum correlations. Its role in several tasks in quantum information theory like quantum cryptography, quantum dense coding and quantum teleportation is indisputable. The role of entanglement in quantum algorithms has also attracted enormous amount of attention in the literature. The research in this direction is motivated by the finding that a quantum computer can efficiently factorize arbitrary integer numbers. Since no classical algorithm is known today that can solve this problem efficiently, this example clearly demonstrates the superiority of a quantum computer compared to its classical counterpart. In this context, entanglement also plays a crucial role: if the quantum computer operates on a pure state without entanglement, then the computational process can be simulated efficiently on a classical computer. In this case entanglement is the key ingredient that makes the difference between a quantum and a classical computer.
However, the situation is more involved if the computational process is not perfect. In this case the quantum computer operates on a mixed state, and the role of entanglement is less obvious. A seminal result in this direction is a quantum algorithm known under the acronym DQC1. This algorithm operates on an almost maximally mixed state with vanishingly little entanglement. However, DQC1 can still perform tasks efficiently for which no efficient classical algorithm is known today. Thus, it is reasonable to assume that entanglement in general is not related to the efficiency of a quantum algorithm.
Triggered by this observation other kinds of quantum correlations have been studied. In this context a particular measure of quantum correlations known as quantum discord is referred to frequently in the literature. Quantum discord is a measure of quantum correlations beyond entanglement, i.e., a quantum state can have no entanglement, but nonvanishing quantum discord. Quantum discord is also regarded as the key resource in the DQC1 algorithm. Although this statement is still controversial, it was shown under very general assumptions that quantum discord is required if a quantum computer is to show an exponential speedup over any classical algorithm.
In this thesis we give a short introduction into the theory of entanglement and general quantum correlations, and further discuss our results. In particular, we show that two different kinds of entanglement measures can coincide. This result is used to build an algorithm for computing entanglement. We also consider the role of quantum correlations for the distribution of entanglement and for the quantum measurement process. We further discuss the behavior of quantum correlations under local noise, and their monogamy properties.
Quantum information and computation, based on quantum correlations of quantum systems, is one of the promising new fields of physics and information science. Entanglement is the key resource of quantum information processing. However, it is shown recently that quantum entanglement is not the only kind of quantum correlations useful for quantum information processing. Quantum systems without any entanglement can still be helpful for quantum information processing since unentangled systems could have another kind of quantum correlations - quantum discord. Thus, quantum discord has drawn much attention in recent years. Here, we briefly review the concepts and properties of quantum discord. Several measures of discord including the original measure of discord, relative entropy-based discord, geometric discord, global discord, Gaussian discord, are reviewed and discussed.
Quantum entanglement and quantum nonlocality are known to exhibit monogamy; that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove, in general, that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.
While entanglement is a cornerstone of quantum theory and holography, quantum correlations arising from superposition, such as quantum discord, offer a broader perspective that has remained largely unexplored in holography. We construct gravity duals of quantum discord and classical correlation. In both holographic systems and Haar random states, discord exceeds entanglement, revealing an additional quantum correlation linked to the Markov gap and non-distillable entanglement, suggesting holographic states are intrinsically non-bipartite. In black hole setups, discord can increase despite decoherence and persists beyond the sudden death of distillable entanglement. Motivated by the holographic formula, we define reflected discord -- an optimization-free boundary quantity based on reflected entropy -- which remains effective even outside the holographic regime. We also propose several multipartite generalizations of correlation measures. It includes holography-inspired correlations based on multi-entropy, which are shown to be UV-finite and reduce to bipartite measures in the bipartite limit. These results provide new tools for quantifying quantum correlations beyond entanglement in strongly coupled many-body systems and offer a novel approach to multipartite correlation measures.