entanglement generated by the far beyond intuitive pure quantum phenomena such as EPRparadox,Schr?dinger's Equation has been considered not only as one of the significant notions in quantum theorybut also a key of realizing the Super Dense Coding and the Quantum Teleportation in quantum communication.However,recent researches show that quantum entanglement is less likely to account for all the properties of quan-tum correlations.Except for the quantum entanglement,researchers find other non-classical correlations like quan-tum discord,which plays a pivotal role in quantum information and quantum computation and that's why the purequbit-decisive quantum computer possesses computational efficiency.With this clarification,quantum discord com-pletely can be a new resource of quantum computation.In this paper,basic notions and measurement methods ofnon- classical correlations(including quantum entanglement) were discussed and the quantum correlationproperties of the quantum discord in various models were analyzed and compared with the quantum entanglement.Conducting researches on the non-classical correlations in various quantum systems are not merely meritorious tothe quantum theory,in the mean time,may provide some efficient thoughts and motivations for researchers to em-ploy theoretical concepts about quantum correlations for avoiding decoherence and theoretical scenario for the exper-iments.
entanglement generated by the far beyond intuitive pure quantum phenomena such as EPRparadox,Schr?dinger's Equation has been considered not only as one of the significant notions in quantum theorybut also a key of realizing the Super Dense Coding and the Quantum Teleportation in quantum communication.However,recent researches show that quantum entanglement is less likely to account for all the properties of quan-tum correlations.Except for the quantum entanglement,researchers find other non-classical correlations like quan-tum discord,which plays a pivotal role in quantum information and quantum computation and that's why the purequbit-decisive quantum computer possesses computational efficiency.With this clarification,quantum discord com-pletely can be a new resource of quantum computation.In this paper,basic notions and measurement methods ofnon- classical correlations(including quantum entanglement) were discussed and the quantum correlationproperties of the quantum discord in various models were analyzed and compared with the quantum entanglement.Conducting researches on the non-classical correlations in various quantum systems are not merely meritorious tothe quantum theory,in the mean time,may provide some efficient thoughts and motivations for researchers to em-ploy theoretical concepts about quantum correlations for avoiding decoherence and theoretical scenario for the exper-iments.
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.
For many years, the notion of quantum correlations was equated with the notion of quantum entanglement. The wide range of quantum protocols whose extra-powers over classical protocol were shown to originate from quantum entanglement mostly motivated this. For example, it was shown that for certain class of problems, a quantum computer could provide exponential speed-up over its classical counterpart, given that it relied on quantum entangled resources. Recently, however, the requirement of possessing entanglement to perform efficient quantum computation has been questioned both theoretically [1] and experimentally [2]. It appears that a non-classical quantity called quantum discord [3] is all that is required.
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.
One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.
Recent measures of nonclassical correlations are motivated by different notions of classicality and operational means. Quantum discord has received a great deal of attention in studies involving quantum computation, metrology, dynamics, many-body physics, and thermodynamics. In this article I show how quantum discord is different from quantum entanglement from a pedagogical point of view. I begin with a pedagogical introduction to quantum entanglement and quantum discord, followed by a historical review of quantum discord. Next, I give a novel definition of quantum discord in terms of any classically extractable information, an approach that is fitting for the current avenues of research. Lastly, I put forth several arguments for why discord is an interesting quantity to study and why it is of interest to so many researchers in the community.